i played pso (+bb), psp, psp2 and yeah nova.
i would say psp2 has more of a story/better story at least than ps nova.
without any spoilers, psp nova is basically about your ship crashes on a planet, normal techs don't work, you find this weird girl and she gives you 'gran' (now you can use your techs lol)
you work on building your base on the planet.
during the game you try to find what this girl is all about, you try to understand this weird planet you are on (you don't really see any people... what happened to them etc), you deal with traitors in your team etc...
you also work on getting your crew back from 'cold sleep', they are just 'frozen' etc, then you can play with those people in your party. but there are like 600 of them or something, at least 100 200 300... i think it's dumb that they added so many. you can make them do jobs in your base, like put them in the weapon show for example and get you a little discount, nothing incredible. choice is nice but, it seems like a waste of time. i'm not sure what happens if you get them all, i never did.
the more you play (or talk to and help with their quests - some chars appear in the base and you can interact) - the more you play with them in your party and complete their requests, you will build your friendship with them, which has different levels. you could build max friendship with ALL the possible characters, but since there are so many... it's pointless. just pick some that look cool, and use them - or just stick with the main 3, 4, 5, story chars the game gives you. (it recommends what characters to take on story missions)
weapons and techs and stuff like that don't drop from enemies or boxes, you need to craft everything apart from items like monomates, you can just buy those.
even the techs need to be crafted, so if you want to level up resta (healing magic) from level 1 to level 2, you need to pick up items to let you do this.
you can customize the appearance of your weapons a little, like add accessories to them.
the enemies are cool, the 'bosses' are big huge monsters that you need to take down and capture...
as for reviews, i think some i have seen are only like 3/5 or something - i enjoy it, but i can see how it could be better, but yes it is good fun