Now it's come about different ways. In one way a kid who develops Spider-like powers just HAPPENS upon the technology. Ignores the fact that it would be awesome for police use and keeps it to himself. I hate HUGE coincidences like that.
Or in one version he just plain was so super intelligent that he invented them himself after thinking "hey, I got spider powers but no web, why don't I make some?"
Freakin' stupid as fudge. Organic web shooters all the way.
Plus, compared to other fantasy techs the technology is just so outlandish. The ability to hold like a pill sized amount of liquid to create such massive amounts of webbing? IronMan's armor is probably 100x more realistic even with all of it's problems (like Jetpack feet).
At least with organic shooters he can hold this miracle liquid that turns to web in his much bigger than pill sized body.
I hate the tech web shooters. They suck.
You do realize the reason he knows how to make the web fluid is because the spider passed the knowledge of it to Parker via the spider-bite? The mechanical web shooters are so much better because they show how smart Pete is supposed to be (something the other movies did nothing for) and they give him the extra weakness of "oh **** i'm out of web fluid", which is essentially his equivalent to running out of bullets and having no more clips.
Pete's web-shooter tech is ALOT more grounded than any other tech in the Marvel universe. Compare it to Tony Stark's power source for the iron man suit which has a single power source that produces far more energy then it consumes, and is a seemingly infinite power source. Or compare it to ANYTHING Reed Richards makes. Richards makes something rediculously over the top and can pretty much just say "i used magic to help make it" and that's all the explanation you get for his trans-dimensional-scientific-portal-device.
Organic web shooters are stupid because they take away one of the defining characteristics of Peter Parker, and they are an extremely lazy cop out for writers. Also, organic webbing was supposed to be something the Black Suit/Venom had as an advantage, it also takes that away from him too.