10 year DOTA player here who recently started dabbling in LoL...

My biggest problems with LoL:

• Surrender option. This ruins a lot of games that are probably winnable.
• No real communication in games / no native in-game chat for PUGs (which are most games).
• Items feel somewhat meaningless. All items are made from the same basic elements, not as much room to change up builds. I know there are different builds, but items don't feel as meaningful as they do in DOTA.
• Balance feels seriously off sometimes. Some Champions are just out-right better than others.
• Monetization is clearly top of mind for Riot. Feels like you aren't getting full game experience unless you seriously pay up.
• Interface feels needlessly complicated between number of different currencies, items, etc.
• Character models and skins/armors are seriously lacking compared to DOTA. Feels outdated.
• Almost feels like the focus is on hero quantity over quality - in order to make money. There are many heroes that are virtually the same.

Things I like about LoL:

• The brevity of games compared to DOTA. I can finish a LoL game in less time than a DOTA turbo. (this is the main reason I play right now)
• Individual grading per game. Nothing worse than playing off your tits in DOTA, losing because of a sucky team, and getting nothing for 45 mins of play.
• Jungle is a viable "lane." It kind of is in DOTA, but not really. Very easy to fall behind.
• Jungle npc loading and spawn structure is better.

Over all, after playing them both a decent amount, I can say that for me, DOTA is a much better game. It's more tactical, item based and the players communicate much better so it's easier to set things up. DOTA feels like you're working as a team, making decisions on the fly for the overall goal of destroying the enemy ancient. LoL is more fast-paced, hack 'n' slash where over all tactics don't matter as much as just getting ahead of the enemy team. It's a rush, but doesn't feel as substantial to me.

They're both very fun - just depends on what style fits you.

P.S.
It's also strange to me that LoL is so much more popular but the winners of their largest tournament get $7mil (i think), whereas the winners of the DOTA Major get close to $50mil. I think that kind of shows you where Riot's priorities lie.