In this "Force (4th) Day", what are your opinions in both games and why one is better than the other in your point of view?
Or maybe they're equal in gaming value?

Equal

For a long time I would have said Jedi Outcast is clearly the better game, but when I replayed them a few years ago I actually enjoyed Jedi Academy more.
Jedi Outcast has a better story (ok, nothing great, but good enough) and more ambitious level design with some memorable locations. But imo the levels actually have too many "puzzle" elements or sections where you have to jump, dodge obstacles or look for your way in non-obvious places, which would be fine in moderation, but gets too much and breaks up the pacing.
Jedi Academy has an absolutely forgettable story even by the low standards of Star Wars games, and its levels are short, linear and mostly won't stay in your memory. But it has great lightsaber combat mechanics, which are utilized to the full because you face so many lightsaber-wielding enemies (much more so than in Jedi Outcast with its hordes of Stormtrooper trash mobs). It also gets going with lightsaber combat and force power use pretty immediately, no annoying mandatory shooter sections like in Jedi Outcast's first few levels. So I'd say if you're purely interested in the lightsaber combat, Jedi Academy is the better choice.
Both are great games though (as are their predecessors Dark forces and the original Jedi Knight).

Get both. Jedi Academy has a bit more replayability, in that you get to customize your character's lightsaber styles as you go through the campaign, while Jedi Outcast has the better story.

iirc you also get to choose your force powers in Jedi Academy, so indeed, you can customize your character to a somewhat greater extent there.

Jedi Outcast has got the more engaging single player experience, but Academy has the better lightsaber combat. Which is saying a lot since Outcast already has amazing lightsaber combat.
One thing Outcast has over Academy is a perhaps surprisingly meaty pure first person shooter section before you get your lightsaber. Not surprising in a bad way mind you. Surprising in that it is actually quite good as far as first person shooters go. You can still fight from the first person perspective with your guns in both Academy and Outcast, but with a lightsaber and force powers there isn't much reason to.

Overall I felt that Outcast was superior.

That's up for debate, it can get somewhat tiresome to battle through hordes of enemies with nothing but that crappy, inaccurate Stormtrooper rifle. It's quite noticeable imo that the game was primarily designed for lightsaber combat, with the shooting being more of an afterthought.

Sure :) But I think we will have to agree to disagree here since I certainly don't think the shooting was an afterthought. It's not excellent, but to me it was far more on the good side than even the mediocre side. That the game was made with Quake 3 arena's engine definitely helped here (which makes it that much more commendable that the 3rd person lightsaber combat is as good as it is). If I had to criticize it then I would also call some of those early sections a bit tiresome, and definitely too difficult/frustrating in parts. Still, overall I found it very enjoyable as a Star Wars experience from a, at the time, non-jedi character.
After you get the lightsaber however I'd agree more : those levels weren't designed with first person combat in mind. Not that every now and again you couldn't still reasonably indulge in some first person fire fights if you wanted.

Yeah, they're a bit too frustrating imo. It would have been better if you had wider weapons variety in them...and if the guns weren't so inaccurate. As it is, those early levels are actually the most difficult in the entire game imo, and that's somewhat questionable design.
But I agree, it isn't really bad, and the level design even in those shooting sections is well above average.

Neither. Jedi Knight reamins the best SW FPS despite the dated graphics.

There are subtle differences from a quick multiplayer game against bots. Wall jumps and some lightsaber moves are changed plus there seems to be more duel maps and less FFA in Academy.

Both are great fun and among my favorite SW games, but Jedi Outcast is better. It's a "bigger" story, it feels more cohesive and more like it belongs with the movies. Academy feels more like a young adult spin-off. It's a lot of fun, it has some great levels, but it's very episodic, the stakes never seem high, the protagonist is a blank slate with none of Katarn's charm. But it serves as a good post-script to the series. I like leaving Kyle as a master and a teacher right beside Luke (the real, pre-Disney Luke).

Yeah, I really loved it - the levels, the FMV cut scenes, the story (such as it is), but I barely used the lightsabre outside of the duels. The improvement between JD and JD2 on that score is absolutely astounding.

Still, to be absolutely honest, while I'm glad I played through the whole series, I think I'll only ever go back to Jedi Knight II and Academy. They are just much easier to get into.

I'm gonna say Outcast, mostly because it is the one in which you can enable lightsaber dismemberment. And also because Kyle was a good character which got sidelined in Academy. That might be more of an operator issue. You know that the E-11 also has an accurate primary fire right? You don't just have to spray everything with the secondary. Just saying that I had no trouble hitting things in any of the games.

I know about the primary fire mode (and that things like crouching and aiming for the heads of Stormtroopers help)...if you use the secondary fire you can actually easily run out of ammo without hitting anything, and then you have to use that stupid electro-taser in melee...
Primary fire however is somewhat slow iirc, so you have to keep a distance to enemies and play very carefully (storming into a room can easily get you killed, because the primary is too slow for quickly killing enemies, while the secondary is too inaccurate and wastes too much ammo)...I found that somewhat frustrating.
Anyway, I'm certainly not a top class FPS player. But imo those early levels really do suffer from the fact that you don't have many options (it's basically just your pistol or that Stormtrooper rifle, with a few occasional thermal detonators)...they go on for a bit too long given that lack of variety.