Ehh, there were a lot of practical choreography that went into the fights, but lots of string-fu, too. In fact, most of the "impressive" stuff seen in The Matrix was either aided by or buffered by CGI/strings.
From a technical perspective, sealgal72 is correct. Keanu, Moss, nor Fishburne were pulling out moves equivalent to what Seagal or Van Damme were doing WITHOUT special effects or wire-fu. The back-and-forth roundhouse kicks Neo did in Matrix: Revolutions, for example, were done with CGI. Many of the throws and flips that were done were aided with CGI/strings.
There is truth in the fact that Seagal/Van Damme torpedoed their own careers (Van Damme turning down a two-picture deal with Universal, and Seagal becoming his own writer/director and ruining any box office mojo he earned up until Under Siege). But everyone and their mama becoming a kung-fu legend thanks to CGI/string-fu is more true than anyone might like to admit. It gave Angelina Jolie her first blockbuster start with Tomb Raider, turned a 90lbs Kate Beckinsale into a badass in Underworld, and helped every average-man become an action star (this was also thanks to shaky-cam with quick-cuts, which is how the Bourne series managed to make Matt Damon look like an action star, even though he admitted he had a tough time learning the choreography and looked pretty poor in the behind-the-scenes footage trying to fight).