AFAIK, and anyone can feel free to correct anything that's wrong in this:
Payoneer was an alternative to Epassporte (ie, it existed at the same time, and has been around for 5 years or so), and started off, or was primarily, in the mainstream (non-adult) world, whereas Paxum appeared as a replacement/successor to Epass when Epass imploded.
Apparently Paxum asks for scans of your ID all the time, judging by all the threads about it here, and has had all kinds of dramas, which usually eventually get forgotten about/resolved. They seem to have quite a few critics but also quite a few fanboys here (who will no doubt reply to this thread). Payoneer is rarely mentioned here.
Paxum seems to be used by more adult programs than Payoneer, though most cam and dating sponsors seem to have Payoneer as an option. I'm not sure if Paxum is also used by mainstream sites, like Payoneer is, but I don't think so.
Oh yeah, I believe Paxum is a penis pill company, whereas apparently Payoneer is the card of choice of Mossad.
As to why use both, why not? They're both free. (AFAIK)
Edit: I dunno, maybe Paxum has a setup charge. I think Payoneer is free anyway, but don't quote me on that. Oh, and they both use the same bank in Belize or somewhere.
I wouldn't take the word of people here about "lower fees", BTW, there have been threads where Payoneer has claimed to have no fee (for something I've forgotten - but maybe to do with wires) that Paxum has, even though they have the same bank. So your best best is to check their websites for their fees, rather than relying on the word of people here who probably don't know exactly what kind of fees there are.