I came into both games fairly late, tried them both, and so far I can't really find a single thing I really like with LoL over Dota, except maybe for cosmetics being more appealing.
Some personal pointers
*Dota has more interesting heroes, spells and items. For example there is a lot more usable items which can greatly alter the role and flexibility of your hero
*Everyone starts fresh, there is no talents or mastery system you only get by leveling up which gives seasoned players a disadvantage. No free wards or blinks depending on what trinkets you choose or town portals that can be used at any time to get back to base.
*LoL has no courier, tp's or secret shops wish diminishes the flow of the game.
*Dota has better interacting between the heroes, like taunts and dialogue which adds to the flair of the game. LoL has these too, but I hardly ever managed to trigger them. Dota 2 also follows Blizzards tradition of adding a ton of pop culture references into the speech.
*All heroes are available in Dota for free. Playing single draft is how I learned the mechanics of nearly all the heroes, which was impossible in LoL because it's highly restrictive with free rotations unless you're willing to pay. Despite LoL having a much greater selection of heroes, the hero variation during my games was almost always the same.
*Dota generally has much faster loading and a functioning pause system with no option of surrendering. It's so frustrating to finally get a good game, then having the other team conceding.
*Custom maps has a ton of fun games for free if you're up for something different.
*Hero guides. The game has a built in guide system with plenty of custom guides to choose from which will help you with item selection and teach you how to best use your abilities. An incredible tool if you want to learn new heroes.
*A true F2P game, which will never give you an edge beyond cosmetic changes.