I wouldn't say that. I'd say Snake takes it, but certainly not with ease.
Raiden took him for these reasons....
1. He was trained by Solidus, he knew exactly what Solidus knew, as Solidus puts it, "I've taught him everything I know", plus that he has had hardcore VR traning and new skills taught in the "new FoxHound".
2. He had a vibroblade, which actually matched Solidus vibroblades. Snake hasn't got anything to parry his swords...
Now if this is Snake in MGS 1 TS, then he is damn agile, and since he was able to keep up with Gray Fox and beat him, I'd say he's damn more than capable of keeping up with Solidus. (Who Raiden OUTSPEEDED to win)
He can do massive leaps, like jumping up to the knee of MG Rex! (Which is like a tall building). He could easily avoid him, and is faster except if you are talking about quick dashes with those jet motors Solidus has.
Snake can also move as fast as normal (not gameplay, he does it several times) with a Stinger missile on his back, and it'd be damn hard for Solidus to actually counter that. If he uses guns he'd have to aim for the head.
Snake also stood up to Gray Fox when Gray had a sword and Snake was unarmed, and did a damn good job actually taking him down several times. Gray Fox is better than Solidus blade to blade (I think we've discussed that here) and much faster in moving his arms, so I think Snake could dodge several strikes. Or do a Raiden move, (quick dash to the left when Solidus strikes) which leaves his achilles heel (his spine or his head) vulnerable for damage....
Since Snake normally does not wield a HF blade (although he does wield one in Acid, I think he started to dislike blades by the time he saw Fox die), I don't think he'll have one, at least not if it is TW or MGS 1 Snake. It's not necessary for him to win though...
I think Snake could very well win, but it'd be a hard fight, and I think there is a big possibility that Solidus would take it like 3 or 4 times out of 10.