Haven't sdeen Matrix Reloaded yet. but have seen (played) Enter THe Matrix.
(which intersects and has around 1 hr of additional footage (cinematic that is, there is also an assload of cgi cutscenes in addition to the extra cinematic rreallife footage, so several hrs of Matrix'nes) that fills out the story a lot more)
(it's advised to play thru the game before seeing the movie)
The Matrix
The Matrix: Enter The Matrix intervowen with The Matrix: Reloaded.
The Matrix: Revolutions
While the Reloaded movie focus on the main things,
the game follows side storys a bit more.
Will be interesting when I see Matrix 2 and how the "missions" and sub stories and info fill out the gaps in the movie.
(spent a full day 20+ hrs straight playing Enter The Matrix lol)
Man I love wall runs, jumps, wall kicks. flips.
And bullet time rawks. seeing the sonic bullet paths is kickass.
"The Brothers" directed the game, original cast took part as well.
And GAWD do I hate Agent Smith. agents are pesky regardless but Agent Smith freaks me out. (so wanna nuke his ass, grrrr)
I did kick his ass a bit now and again

couln't take him down tough lol...
I did send one other agent flying over a rooftop splattering into the ground tough lol...
And I got to assist Morpheus, saving his ass lol...
there is a hacking interface in the game. some people says that
in the movie Reloaded there are codes seen on the city signs
that can be used to enable hidden features (i.e cheats) that will
unlock the full potential (i.e you reprogram the matrix itself hehe
While Reloaded shows from one angle/pov what happen,
Enter The Matrix shows it from another angle/pov.
If ya loved Matrix. you'll love Enter The Matrix... highly recommended.
Ah and if ya see an Agent. RUUUUN like hell, go for that hardline phone! lol