I may get some stuff confused with FFL 1, but I played FFL 2 and a friend, as I said, still plays it a lot. I don't think there's experience. In 1, you had to buy items to increase stats for humans, and mutants gained stats from actions in battle (i.e., use a heavy sword, strength goes up; defend [and get hit], defense goes up; use magic, mana goes up). In 2, I think both mutants and humans improve stats that way. Monsters and robots get more powerful by transforming into stronger monsters and robots by eating meat or attaching parts dropped by enemies.
The other big difference in classes are inventories. You have a party inventory, and each character has an inventory. Character inventories get filled up with equipped armor and weapons to use. Humans have as many slots as the party inventory. Mutants have at least four slots taken up by special powers (I think it's four free slots, four reserved slots). They may be passive resistances (or even weaknesses), or they may be exceedingly awesome attacks. In FFL 1, the powers changed randomly (or seemed to), which meant you could be kicking butt counting on your mutant's ability to rain death, then suddenly find yourself running from everything because your mutant has decided kicking but is too much trouble, and he'd rather develop the ability to die from a single fire attack. In FFL 2, you have a little more control, but I don't know the details. Finally, monsters and robots have no free inventory slots. They're all reserved for special powers, even if the monster or robot doesn't actually have enough powers to fill them all.
The plot is fairly disjointed. It starts with your adventurer father popping in to tell you something and then leaving again, for good. After a while, you decide to go look for him. You go to school, pick three classmates, and head off. You climb some sort of thing from world to world. FFL 1 had the tower to paradise, I know, but FFL 2 had something like a giant celestial rope or beanstalk. The goal is to collect the pieces of a broken goddess statue before they fall into the wrong hands (I had to look up that part). Each world has a subplot, usually with an NPC joining the party for a while.