Karas might also apply, whether that thing is magical or mechanical is anyone's guess though.
Armored Trooper Votoms kind of blurs the line a bit, in regards to size, the ATs are more akin to big powerarmours, but in function they appear more as Mecha (None of that flying, beam-spamming stuff though.).
At their simplest, Guyver: Bio-Booster Armor (which I second) and Apocalypse Zero are anime about a guy in a living power suit that fights monsters and opposes an evil organization.
Guyver does away with the over the top gore of apocalypse zero and instead comes up with more story and character development. Regardless, if you enjoyed the battles in Apocalypse Zero, you are sure to enjoy Guyver.
Blue Gender and MD Geist follow a similar line , War on Earth , Death on large scale counts , Humans colonizing space , Soldiers having battle armor suits , A corrupt goverment official or officials. Yuji is much like Giest , Rising up against wanting to live in space , Earth is where humans belong and both fight for this reason. All the mech-style , Fully loaded heavy artilary tanks , Armies with massive destructive capabilities.