Jedi Academy use the same engine version though different build and customized as much as the Jedi Outcast's version. Updated graphics is the most basic change naturally.

The very core of the gameplay is the exact same. Most of the weapons got only balance changes like projectile speed or spread ratio. New weapons got introduced however most of the tools got removed (like the energy wall projector and the carriable medpack).

The lightsaber combat received the most radical change. To start with you can use two sabers or staff. All those have advantages and disadvantages in certain areas whie the single saber is the middle ground thanks to its versatility. The chaining works a bit differently and now you can perform simple attacks from more varied angles. I don't really want to go in depth so the more slower a slash the more harder to parry it while the heaviest attacks may easily go through the blocks. The different stances have different values for that so one may block something the other can't.

Overall it is much easier to fight lightsaber vs. lightsaber battles thanks to the higher degree of freedom of the attacks. There are new Force powers to help exactly where it needed.

The handle of story also a way different. To start with you start the game as a Jedi and have a lightsaber as well. Jedi Academy offers missions rather than making you play through linear stages. These missions takes place on separate openworld maps, some offers more freedom while others are linear like in Outcast. Usually it takes not much time to finish a mission however after a set of five there is a story mission which is longer and takes place on multiple maps and feature bosses at the end. The only map I found confusing is the speeder bike one and only for first. It is always clear what to do and where to go though not always the "how to do so".

Even the most difficult missions are less frustrating than the one you mentioned. No sniper spam, no surprise spawns from impossible angles, and no alternative physics for certain missions (no zero gravity or swimming parts). Most NPCs are pre-spawned on the map so you can play strategically if you want to but even if you not care about memorizing, it is easy to spot where they attack from, especially the snipers. The mentioned new Force powers also exactly covers this making Force Sense a very big help for seeing incomming attacks.

It is questionable which game is the better. I really liked some of the stages of Jedi Outcast but I enjoy trying new ways in Jedi Academy too. When I said easier lightsaber combat I didn't meant it is easy to beat some of the Siths. In Outcast you have to rely on skill and reflex only against the stronger enemies but Academy give you some techniques that makes it doable tactically rather than with brute force. I enjoy mixing it and honestly I miss this when I played Outcast again.

I can't count how many times I finished Jedi Academy, one of the few PC games I always replay times to times.