Basically, they both add treble. The exciter generates upper harmonics from midrange frequencies. This can work well on sources that lost their treble - like cassette tapes. For guitar you're adding harmonics to the ones that are there. Maybe you like it, maybe not. I don't generally care for it. But if you use it, be careful. It often happens that you get used to it, crank on more, get used to THAT, etc... repeat until your ears bleed from treble overload.
The Maximiser claims to "realign" bass & treble in time to give greater clarity. This is pure bunk. IIRC, this was originally designed for hi fi systems with 3 way speakers that usually have drivers mounted on a flat face. In this arrangement, the sound from the woofer actually originates an inch or two behind that of the tweeter, which this purports fo fix. Unless you're sitting in an EXACT sweet spot and never move your head, the distance they claim to fix is the LEAST of your worries. And on guitar rigs where there's one speaker or 2 or 4 that reproduce the same frequencies, even the theory makes no sense.
So why does the maximiser make audio SOUND brighter? You may have guessed - it also has a harmonic generator. Theirs sounds a little different than the aphex, and I actually slightly preferred it on program material (like brightening cassettes). But they're similar.