If you are pitting the two characters against one another then you have to 'normalize' the rules of the universe they pit against each other in.
In Spider-man's world, master ninjas (without other additional powers) don't take apart tanks with their bare hands or break the laws of physics
If you use Snake Eyes as the context, you have to admit that he is a regular human who has honed his mental and physical prowess with training. That being said, he still has hard limits.
Spiderman is a genetic anomaly. Canon says that he has way above maximum human strength. Whether his reflexes are better than Snake Eyes' reflexes is debate-able.... but a moot point because of his spider-sense. So at the very least, he will be able to react as fast as Snake Eyes does. Spidey's speed (movement) will be faster than Snake Eyes' by virtue of his strength, smaller size and lower overhead (no equipment or weapons to carry except for web-slingers).
Seeing as how Snake Eyes can dodge arrows and ninja stars, I find it unlikely that Spidey will web him up unless it is from very close range. Snake Eyes' sword makes him more dangerous at close quarters, but Spidey's strength makes fisticuffs a losing proposition for Snake Eyes.
For argument's sake, I might agree to Snake Eyes being roughly as agile as Spidey, but without the ability to wall-crawl.
Its not clear cut, but seeing as how Snake Eyes hardly poses a physical challenge to Spidey, its hard to see how he would eke out an outright win. Spidey's real obstacle would be Snake Eyes' tactics and training...
I say that a Snake Eyes equipped with firearms would be too much for Spidey to overcome, and that a Snake Eyes without guns would be outclassed in terms of stats (power, speed, agility).
Spidey with the black venom suit would destroy Snake Eyes in any head-on clash. Period.