The normal map for Infinite Crisis has capture points, arranged in a ring, you can move through the center of the map where there are speed boost pads and nobody can see by default unless they slap down cameras or the like. At certain times an "orbital cannon" unlocks for capture, but it drops larger sieging robots and blows up some map terrain (and presumably anyone standing there, although I've never seen anyone be hit by it) - although the last time it fires it blows up the center of the map and causes a huge shockwave. I haven't tried the pvp-playable map type.
As for comparisons to LoL or AoS/DotA, the only thing I've really played much is LoL, and then only to player level 10. From what I remember, in LoL there was one normal map that everyone played, which had three paths, towers galore along said paths, and some kind of community-defined rules dictating that certain characters must always go on the top lane and others on the bottom even though both lanes looked identical. I vaguely recall there being some kind of capture-point game type, but apparently playing it was frowned upon for some reason that was never really explained to me (aside from "if you play it, you're a [Censored]"). I was much happier quitting than I was listening to all the players bitching that I was playing incorrectly (meaning I was trying something different, experimenting, or when I was playing Nidalee, which was most of the time, because I was ignoring the meta and going where-ever there were vulnerable targets or allies in need of assistance instead.