Some players came to LoL, play a lvl 1 game, reked noobs, "huh this game is easy for noobs blah blah".
Then he went to Dota, when it was still the original mod or when it hasn't implemented a proper matchmaking balance, got rekt, "this game so hard cool better than that trash lol pos".
But really though, both games play out similarly because they are in THE SAME GENRE. Idk why some people just have to complain that LoL is similar to Dota, let's just forget that there are like 10 trillion FPS, RTS, RPGs, MMOs, Hex Grid RTSs, Shoot'em Ups, Beat'em Ups etc you get the idea.
The "rivalry" is a joke, you laugh at jokes, that's what you do.