Apologies to Krensky for being a dick in my response upthread. I guess I was in a bad mood, and after I posted it I decided to take some time off from the interweb. Sorry about that.
So, on review, I guess my issue with using Cyberpunk 2020 as an example of what to do with cyberpunk is that I found it too focused on the props and too all-inclusive. I think Shadowrun went the same route - possibly even further, given that it was also fantasy. Since those two games became sort of the standard for the genre (and many people's introduction to it), I think it skewed audience expectations toward games that featured tons of equipment, cartoonish violence, and generally what feels like a caricature of High Tech Low Life rather than something tied to the stuff that interested me in it in the first place.
Science Fiction games and modern games tend to lavish a lot of love on gear lists, really. Its maybe a kind of escapism or empowerment that doesn't seem as "unrealistic" as mutant DNA or magic? That is to say, you can play a fairly "normal" person who just happens to have some amazing gizmos and fetishy weapons to let them do great/terrible things. I can get into that up to a point, but in my experience Cyberpunk PCs tend to have crazy priorities when it comes to that stuff. I distinctly recall my runner teams getting something like a quarter of a million dollars in pay from their assorted Johnsons - then turning around and dropping ALL the cash on wolverine claws, super-duper reflexes, and loopy custom model firearms. When you consider that these characters were depicted as living in awful, oppressive metroplexes and doing a job that was thankless and incredibly hazardous, it always made me wonder why they didn't just take that same money and, y'know, retire to a private island. Obviously, OOCly the players wanted to keep playing but with Kewler Stuff, but it never made much sense from a character-based mercenary or criminal mindset.
The violence didn't bother me as much, as I like action movies as much as the next guy on these forums. I just wished it hadn't become so perfunctory and acceptable as a modus operandi when these so-damn-slick solos and netrunners were meant to be doing fairly subtle work on behalf of companies. Its kinda of a rule that Carefully Made Plans in spy/heist/cyberpunk campaigns WILL fall apart at the first opportunity and devolve into a firefight; that's backed up by some examples in the genre, really, but I think it encourages metagame thinking that puts firepower way above brainpower and leads to absurd uses of force a lot of the time.
The caricature was probably inevitable. Even in their earliest incarnations, CP 2020 and Shadowrun featured pretty broad and shallow takes on their settings and the characters in them. CP 2020's Roles were neat from a team/niche standpoint, but they were pretty rigid and based on surface flash rather than any internal logic. Even if you and your players dug deep and invested them with lots of personality and backstory, the kitchen sink setting encouraged style over substance every time. That's consistent with the stated intentions of the game (at least Pondsmith's), but I think it ultimately did more damage than good. Its hard to take the day-to-day existence of a Cop very seriously, for example, when criminal gangs are armed like government special forces and themed in ways that would look kinda goofy in an issue of Judge Dredd.
I have played and enjoyed games in the over-the-top realm of tabletop cyberpunk games. They were fun if wacky. I just think that it might be worth stepping back, reconsidering their origins and what those things were about before accepting what we got in those earlier attempts.