Let's see... Cain and Able plots in the backstory, (Mata-Nui or Ekimu vs Makuta; Celestia vs Nightmare Moon) six elemental heroes, (admittedly the MLP protagonists have rather different elements than the classical ones we're used to) the aforementioned evil queen controlling an insect-like horde, (Roodaka; Chrysalis) a Captain of the Guard voiced by the same guy, and until the end of Season 3, all signs seemed to be pointing toward the protagonists sharing a single destiny, though what that would be is still up in the air.
Also, then you get into the generations, which I've done a fair bit of research on.
"My Pretty Pony" - Galidor (bad precursor)
MLP G1 - Slizers/Throwbots (pretty good but not fully fleshed-out and commonly underrated)
MLP G1.5 - Roboriders (bizzarre followup that some fail to realize even existed)
MLP G2 - Bionicle G1 (actually these are sort of polar opposites given that MLP G2 had no story or show at all, while Bionicle had tons of it, but whatever.)
MLP G3 - Hero Factory (not terrible, but still kind of bad and wasted its potential on inane 'plots')
MLP G3.5 - Ben 10 (terrible in every way. Kill it with fire.)
MLP G4 - Bionicle G2 (lookin' pretty good; takes ideas from older generations and adapts them pretty well)
And then of course there's the fanbases, where there's a ton of guys, most are pretty cool people, but then you have a very loud minority who give everyone else a bad name. And people unfamiliar with both tend to judge them negatively. ("Isn't that just like Barbie?" sounds rather similar to "Isn't that just like Power Rangers?")
So, yeah. I'd say they're astoundingly similar; one just has more rainbows and the other has more explosions. Although the former has had a few rainbow explosions in its latest incarnation. Probably the biggest difference is that MLP's best episodes are usually the ones that have nothing to do with an overarching plot, while Bionicle's plot is basically unavoidable and pretty good besides.