I've said it before and I hold it to be true today.
Metal Gear Solid for the PSX is the greatest video game ever made. It was light years ahead of everything else that came before it, and there are game designers working TODAY, ten years later or whatever, that can't make a game as good as that. It's not my personal 'favorite' (that would be the Resident Evil series), but just as I, as a Cubs fan, must recognize Albert Pujols or Alex Rodriguez as the best players in the game today, I as a Resident Evil fan acknowledge that MGS is just superior.
I also enjoyed Twin Snakes immensely, but the MGS2 style gameplay and enemy AI is not suited to the smaller environments of MGS. Granted, I think the story was better and more complete, and I had NO problems with the crazy action cutscenes whatsoever (if Solid Snake is of the same ilk as Foxhound, why shouldn't he be able to do some of the same stuff?). Twin Snakes is simply the better version of the story, from the cutscenes to the dialogue to the presentation. Period. The gameplay is 'really good', but it's not as balanced as it is in MGS.
So it really depends on why you play MGS. If you play for the storyline and characters, then you absolutely MUST play Twin Snakes, because that is the official version of the story in terms of continuity. Bear in mind that the story of the original MGS is not really all that different from Twin Snakes, but Twin Snakes is a more grand presentation. Personally, I recommend you play Twin Snakes right now. With MGS so fresh in your mind, it will be easier for you to pick up the idfferences if you are playing to enjoy the story.
But if gameplay is all you play for, stick with the original. Much more balanced version.