I feel as if comparing League and Dota 2 are similar to comparing a game like Yugioh to Magic. (League/Yugioh compared to Magic/Dota)
So in my opinion , League is somewhat of a prettier game, while I feel Yugioh artworks and rarities are nicer (in a different way) than the artwork in Magic. While the Dota map(S) aren't ugly, they aren't as aesthetically appealing to me. (Not saying I dont like the Dota map appearance or MTG artwork, I just prefer the other over it).
I realize now comparing these 2 to 2 TCG's might be a bit harder than I thought.
Now, Yugioh to me seems a lot more friendly to a wider audience. The artwork is very appealing and you can argue the game is easier than Magic. Yes Yugioh does have chain orders/weird rulings and a lot of potentially complicated combos to pull off, but Magic also requires you to manage your mana and creatures over your turn and your opponents, the main difference being your cards have costs and different strength/weaknesses to the abilities other creatures may have (flash, reach, flying etc).
Comparatively, I think League is prettier and a lot of the champions are more simple (while some are more complicated), and is more friendly to a wider age range (unfortunately). While in my opinion, DOTA is like Magic, because they both (once again, imo), require more strategy to be played at a higher level.
(Briefly back to the art thing. I think League and Yugiho compare because their art styles are typically very vibrant. Like monsters in yugioh look somewhat badass and half of the females are aesthetically appealing, meanwhile in DOTA/MTG, the map is a bit grungier, just like the artwork. The undead actually look undead and the artwork tells more of a story and kind of shows the effect, rather than just showcase a badass picture of the monster).
I realize now that it was a lot easier to simply compare the 2 card games and add similarities of the 2 MOBAs between them. Then, again, I realize that people who don't play MTG or Yugioh will have no clue what the fuck I'm talking about, so I just wasted like 8 minutes typing something that most people won't understand, and even the people who do understand, will have a hard time reading it because its 6am and I can barely even understand what I'm saying.
TL;DR: at the end of the day, it comes down to play preference imo. Both are decent MOBAs with their similarities (as all mobas have), and then their differences.