They both have their merits and downfalls.
GOOD:Dota has:
-All heroes free at all times
-Very balanced hero selection.
-The ability to deny the enemy gold and some xp by the killing of your own creeps when they get low with a last hit, and even your own ally heroes if needed.
-A team from Valve who are known for their customer service, good will, work for balance, and the inability to count to 3.
-A (atleast on average for me) nicer community than most MOBA's.
-Modes like ability roulette(needs some tweeking and banning of certain heroes, but still fun) And single draft to keep games interesting and fresh.
-A case by case report system.
-Available on PC, Mac, and Linux
League has:
-A huge character roster that is still being updated today.
-An entire game studio dedicated to its development
-Several different maps (Even if disputed about how good or bad they are)
-A unique rune system that serves to allow further customization of champions outside of in-game item builds
-Instant turning
-Its own fresh match ideas such as ARAM, and that circular mine map where you take the points. (Name escapes me)
-Enormous player count
BAD:Dota has:
-A couple broken characters. (I will argue Terrorblade OP for days, and Sand King on occasion.)
-Several, though rare, bugs with the item guide selection and uploading; as well as the hero selection.
-A rather... finicky replay saving system
-Untradable and/or sellable items
League has:
-A reputation for broken heroes (Though this is getting better, still, Jax.)
-A hero rotation that, although good in theory, requires you to work to buy a character you enjoy playing a lot
-A VERY vocal and angry community, who will critique anything not to their liking, or if it doesn't work.
-Really heavily based in meta
-PC only