Basically, Spiderman “goes dark” because of the suit, not vice versa.
I’ve never followed the Spiderman comics much, but I think the movie (which I saw this past weekend) took plot points about the “symbiote” from the mid-90s animated series more than the comics (box contains movie spoilers, but no major plot points that aren’t in the trailer):
[spoiler]The symbiote came from space. In the animated series, it came down on the shuttle (piloted by Jameson’s son) and IIRC caused the shuttle to crash, Spidey picked it up while saving the crew. In the movie, the ooze pops out of a crashed meteorite.
I’m pretty sure the animated series had Peter consulting with Dr. Conners about the properties of the “ooze”. Conners discovers that it reacts strongly to “darker” emotions (especially anger), and has the abilitiy to bond itself to a host. The movie has similar scenes.
The black suit increases Spidey’s powers. He’s stronger, faster, and has an unlimited supply of webbing (in the comics / animated series the webbing was a chemical that Peter invented, he often ran into trouble when it ran out). This power, along with the symbiote’s mental infiltration, made Spiderman more arrogant and less caring.
I don’t remember the inciting incident in the animated series, but Peter eventually fought off the symbiote in a bell tower, using its sensitivity to sound to weaken it. I’m pretty sure he did this deliberately in the series, in the movie it was more of an accident.
After being rejected by Peter, the symbiote latches on to Eddie Brock. The symbiote gave Eddie Spiderman’s powers, along with knowlege that the symbiote learned from Spiderman (including his secret identity). In the series Eddie was a much bigger guy, so Venom was physically stronger. Also (and this was never explicitly shown in the movie, but there are subtle things that can be interpreted this way), the symbiote is able to “cloak” Venom from Spiderman’s “spidey sense”, making Venom one of the few villians able to really get the drop on Spiderman.
Eddie / Venom is much more of a “fused” personality than Spiderman / symbiote was. IIRC, Venom usually spoke as “we” instead of “I” when talking.[/spoiler] Now, how “canon” the animated series is may be up for debate. 