Welcome to MxO.
Well, you're presented with quite the quagmire.
Vector is as 'real' as it gets on MxO. From level sixteen, you're permanently susceptible to PvP, whereas on Syntax and Recursion, you have to type /pvp in order to manually 'flag' (become susceptible to PvP, which wears off after five minutes of being combat free). As has been said, Vector's overbearing focus is PvP, with a minority interested in RP. The RP that does occur, however, is usually relatively isolated.
On the other hand, Syntax and Recursion are essentially split down the middle. Syntax has been referred to unofficially as the 'RP server', though I've seen no more evidence of that than on Recursion. There's just as much, if not arguably more PvP on those servers (simply because people tend to stay away from the main PvP area on Vector if they don't have others from their organization to even up the odds. On the other servers, you can hang around the main PvP area freely, and PvP breaks out more readily), but as it's a choice, you don't get that feeling of immersion as you do on Vector. Here, you have to eternally watch your back, and be wary of going near other players at all times.
It really depends on what your main focus, or interest is in. There's plenty of PvP on the non-hostile servers, as well as RP. However, Vector is more immersive, and if you can locate some RP then you have the best of both worlds. The RP's just a little harder to find.
Hope this helps, Dante.