DOTA2 has more things to manage and requires more skill; if you start with League you may pick up some bad habits that could make DOTA2 more frustrating to learn in the future. On the other hand, if you start with DOTA2 you can move to League with relative ease. DOTA2 has a more competitive community and is generally viewed as the real deal, while LoL is often looked down upon as a casual's game.
DOTA2 has a superior F2P model; everything is unlocked from the start and absolutely nothing you can buy affects game balance in any way. There's also no persistent elements outside of the game, so there's zero difference between the accounts of someone who just installed the game and someone who has been playing for 1,000 hours.
I prefer DOTA 2, but I also have more time into it - I've only unlocked like 2 or 3 extra heroes in LOL. LOL only gives you 10 random heroes (rotating randomly each week or so), but you can spend in-game points or real life money to permanently unlock heroes you want access to at any time. You also spend in-game points or real money to upgrade them with fractional improvements from runes, etc. That structure just kinda bugs me. You basically have to either suffer through playing using heroes you can't stand or that aren't good for beginners until you have enough points to unlock someone you actually want to play.
DOTA 2 does indeed give access to every single hero from the start, all the time. There is no pay to unlock or pay to win. All the purchasable stuff is cosmetic and fully unnecessary for the game.
DOTA 2 is a bit steeper to learn - probably - although I can't really say for sure since I had already played DOTA 2 a bit and was familiar with MOBAs before trying LOL. I don't know how it would have been if I'd tried LOL first.
Basically, I'd say it boils down to trying each out, and then going with whichever one you like better. Both have practice mode with bots, so you can try it out before jumping online with other people. Just understand and expect that you're going to suck and not really get it at first. If you can find someone to play online with that you *know* and practice against bots, and they can coach you a bit on first-time setups and how gameplay works and stuff, it makes it much easier to learn.
"How do I get rid of a Trojan Horse?" -Sailor_Kakashi "Leave it outside the gates of Troy overnight." -Davel23