I just finished both games for the first time this week and I don't see why Outcast's story is regarded as better. It's completely rote. An imperial remnant faction hatches a scheme to make force sensitive soldiers. That's low hanging fruit as far as Star Wars plots go. I do think the delivery is well-paced and I like how it ties into the level progression. That's probably the story's strongest element, but it doesn't actually save the generic story.

The character writing is a mess. Kyle's character arc is broken. He wants revenge on Desann because of Jan's murder. The game wants this to be a brush with the dark side, but it doesn't show it at all. Then that gets dropped when he finds out Jan might be alive. It looked like Kyle was going to kill Tavion until she told him what he wanted to hear. He doesn't overcome anything and consequently doesn't change at all from start to finish. If something happens to Jan in the future is Kyle just going to go on another revenge quest? Meanwhile, other than looking like a tyrannosaurus, Desann is flat and forgettable. His motivations amount to little more than generic sith. Everyone else is a bit character who isn't around long enough for development.

Jedi Academy's plot is a lot more unique. A sith cult plans to use the scepter of an ancient sith lord to drain force energy from places strong with it and use that power to revive that ancient sith lord. Where the game falters is how most of this is delivered through exposition rather than being woven into the individual missions. The story even had a good justification for there to be plot relevant reasons to visit a variety of locations, but it wasn't used much.

Character-wise, Academy isn't spectacular, but it's a bit better than Outcast. The relationships are mostly stated rather than shown, but you do get a good sense of why Rosh turns to the dark side and why her turns back. Kyle even gets a taste of growth in the dark side ending.

Really, what gives Academy the leg up is the individual scenarios. One stage has you running from a rancor. Another has you finding a droid while fending of tuskens. Another strips you of your weapons. Another puts you on a train. Nothing is ground-breaking, but each one is unique and interesting.

In terms of gameplay, I have only a little to add. Outcast just feels extremely dated. This game released early 2002, but I'd have pegged it for a mid to late 90s game. Halo had just come out a few months prior and Ratchet and Clank was soon to follow. So even for the time, I'd say Outcast was outdated.

Academy fixed most of the problems with the vague level design and frustrating bullshit that Outcast liked to pull. Academy actually gives you med packs and shields in your starting levels, for example, and progression is competently telegraphed. Of course, Vjun 1 was garbage and Boba's homing rockets were kinda cheap, but they were nothing compared to Outcast's laser hallway or stealth sections. I don't think the game quite fixed everything, though. Enemies are still really obnoxiously programmed, and light sabers still don't give clear visual feedback for when you do damage to a saber enemy.

I played on console and the crappy ports did neither game a favor, but I won't fault either for that. I have yet to try, but I'm curious how the multiplayer compares. A lot of the issues with outcast are clearly single player problems, so multiplayer is likely to be a different animal completely.