I would say that LoL is one of those games that is easy to pick up but hard to master.
I wager several of the players here who are proclaiming that LoL is just 'casual' probably only did a few solo-queue matches. If you make it up into the upper ELOs you'll begin to really see the competitive scene. So LoL is definitely as competitive as HoN and i'd argue even moreso in those aspects.
With that said, I'd offer the OP the advice that if they liked certain features from DOTA (LoS jungle, denying, losing gold on death etc) then go ahead and try HoN.
The difference isn't one of which is more casual or competitive since LoL has ranked now and you can do EM in HoN anyway. So play based on which one has the mechanics you like more.