I think that there's a lot of misinformation with regards to the two games. I'm gonna take the time to clear up a load of things, so everyone is well informed on the two games, but please keep in mind that I'll be expressing my opinion, so if it's not factual, then it might be slightly biased (straight up going to say I enjoy Dota 2 more, but still think LoL is fun).
LoL and Dota are not even the same genre. LoL is a MOBA, and Dota is an ARTS. I think that ultimately, any comparisons are bad, but I'll have a crack at it, because people like bashing the other's game of choice so much.
LoL has a differing business model to Dota, where you can unlock Champions, Skins, and boosts to cut to the chase of playing with whatever Champs you choose to. You can grind, and unlock the Champs for free, but on average, it takes 1.5 years to do that, so spending a bit of money to support Riot is a good idea. Dota has the Hero pool completely available, at all times, but you will be able to buy cosmetics.
LoL, with their business model, is in a tricky position as far as balancing is concerned; at all times, they need to make sure that a new player can choose a Champ that will help his team; you can't have a free Champion pool comprised solely of Carries. So you'll tend to get some overlap in Champion design, the Carry typically has a gap closer (or a slow, to help close distance), a steroid, a CC or sustain of some description, and an ultimate, which does something. Right here, you've got Vayne, Tryndamere, Corki, Master Yi, Nunu, just to name a few.
Dota has no business model that actually effects gameplay, it's going to be purely cosmetic. So you'll get pure counterpicks, and gimmicky Heroes that do just one thing. But that's okay, because nobody is forcing you to pick that Hero, at least at a tournament level. You've got Outworld Destroyer as a counterpick to Anti-Mage, and Silencer as a counter to casters.
League of Legends has to make sure that their free Champion pool for the week is viable for new players. They don't want a player to have an all-carry team, because that would be bad, and they wouldn't have much fun. So they're going to end up creating Champions that are viable in the free Champion pool. The only exception to them *not* releasing the fortnightly new Champion into the free pool has been Urgot, in Season 1, who was not put in because of the difficulty of learning the nuances of him.
Dota is not restricted to that sort of thing, so IceFrog's 2 new Heroes a year can afford to be new, and different. We've got Ancient Apparition, Treant Protector, Shadow Shaman, and all kinds of specialized Heroes that are piss-weak if your strategy doesn't include them. A strategy with Shadow Shaman is going to be different to one with Leshrac, because Shadow Shaman is a pusher with heavy emphasis on disabling, whereas Leshrac is a pusher with an emphasis on AoE damage.
So already, we have Dota being a bit weird, doing things that could spell a death sentence for Riot, because they cannot afford to stuff things up with a bad new Champion. IceFrog pulled the Conjurer from the game, because he was just retarded. Not even worth a remake. I don't recall exactly what happened with the Gambler, but his 1% insta-kill chance made Level 1 Roshans stupidly predictable, and the chance element made him unfun, and unskilled, so I guess he got removed too.
Gameplay, and difficulty and whatnot:
I think that pretty much everyone can agree that Dota is a harder game to learn, and master. So I'll be taking that as fact, and explaining why the burden of knowledge isn't that bad.
League of Legends is incredibly accessible. This is necessary for Riot, because they need money to continue development of the game. Their aim is to appeal to as many people as possible, so naturally, some of the Warcraft 3 mechanics that either didn't make sense, or were just not fun, were removed. This goes from the strange tower aggression, to the strange practice of Orb Walking. Riot's business model makes them want to make the game as fun for as many people as possible, as quickly as possible, to retain appeal. Dota is almost impossible to pick up and play, and is very un-fun if you have no clue what you are doing. So you get Riot making the new players feel as comfortable as possible, so the Health Removal mechanic which doesn't really make sense (WHY DOES MR NOT WORK OMFG PLZ NERF) gets removed, because there's a burden of knowledge associated with that. Most of the skills in League of Legends you can cotton onto pretty quickly, but Bane's Nightmares confused the hell out of me, when I was playing against him, getting nightmared, and playing as him, still getting nightmared. The mana burn from (iirc) Wit's End was removed, because it was not immediately obvious what was happening, and the idea of getting all of your mana sucked out isn't exactly fun to a new player.
Dota, being built upon the Warcraft 3 engine, has a few relics from the past. There's the trees, which can be cut down, forced into, hidden behind, eaten, and are core parts of Goblin Shredder, Nature's Prophet's, and Windrunner's kit. There is a reason why Riot removed trees, it's because that sort of thing is just one more thing to learn. You don't want a destructible environment for new players, because it means that the environment that they are learning in changes, making for a harder and more taxing learning experience.
The spells in Dota work differently to the spells in League of Legends; it's a very bad idea, as a rule, to use spells on creeps (assuming you are not a pusher, and are not pushing.). League of Legends uses spells differently; last hitting with spells is a core part of Veigar's and Nasus's kit. The spells in Dota are balanced so that they are powerful enough to hurt, but expensive enough to not be spammable. A good example of this is Windrunner, who has a very powerful long-range nuke, but, despite being an intelligence hero, which specializes in spells, often goes out of mana. Crystal Maiden, a support, has a global mana regen aura, which, at level 4, provides 2.0 extra mana each second. Now, this may seem underpowered (why take a mana regen when you could take a disable?), but the extra mana that it provides makes you able to put that much more pressure on lanes, sacrificing your late game, for your early game's benefit.
The ultimates in Dota are often situational, but very often, extremely powerful. It's possible to instagib a Crystal Maiden with just Juggernaut's ultimate, but they're balanced. The longer cooldowns, higher mana costs, and more situational effects all make for a higher skill ceiling, and better ultimate. Queen of Pain has a conical nuke ultimate, and her blink, a long range flash, synergizes well with it, repositioning for a better ultimate. Of all the League of Legends ultimates, only a few come close to the game-changing abilities that Dota has; Nunu's channeling ultimate can, if positioned in a bush properly, instagib the enemy team. Tryndamere's ultimate can give him that extra few seconds needed to duel it out. Teemo's mushrooms allow him to split push, and stay safe effectively.
I don't think that the skill and knowledge required for Dota will be an issue when it is released; there's already hundreds of DotA tutorials, which all apply to Dota 2, and they're going to ship Dota 2 with tutorials, and Quests, which will presumably be similar to Tutorials. The play-with-a-mentor function will also help lower the bar.
Burden of Knowledge
It's bound to come up in every single argument about the two, but essentially, if you don't know how to play Dota, and you pick Invoker, you're gonna have a bad time. Morello has his Burden of Knowledge and Anti-Fun mottoes, which justify the removal of mechanics, and honestly? That is completely fine. If League of Legends had half of the anti-fun mechanics that Dota has, they'd go bankrupt, because it'd be raising the bar of entry. Dota, without a pay model, doesn't need to do that, so they can raise the bar as high as it likes. You don't like Dota's high knowledge requirements? You don't need to play. This works for Dota, and it doesn't for League of Legends, and that's as far as you need to go.
I think that there's a lot of silly ideas about how Dota 2 is being monetized. People think that they're going to need to pump hats and such into it to keep the money coming in. The point is, that Valve really doesn't need to. Dota 2 doesn't even need to be a monetary success, I think that their gameplan here is to capture the Chinese scene, which has millions of Dota players, and then get all of those players onto Dota 2, and therefore onto Steam. If they get Steam on even half of the Chinese Dota player's machines, the sales that they get from those new customers will be worth it. And Valve can afford a flop anyway, so they've really got near nothing to lose. Riot is working on only League of Legends, so they've got to keep it commercially viable to stay afloat. If the people decide that a push meta for League is the only option, then Riot is going to have to accommodate that, or risk losing customers / streamers / viewers.
I think that it's worth mentioning that there's actually a lot less work going into Dota 2 than people think; of the 300 staff working at Valve, there are only about 50 active at each time, when Riot has a full 300 staff working all the time.
TL;DR: **** you, I wrote an assload. In essence: League is a business model, Dota is a game, League wants your money, Dota doesn't. Dota says 'if you don't like it, **** off', when League apologizes, and asks you to stay.