The wrap or plating definitely makes some difference.  The metals used all have different density and properties.  Silver for example, is kind of heavy and doesn't have much springiness to it.  Jewelers consider it a fairly dead metal.  Gold on the other hand, is even heavier, but quite springy.  The difference that the metal of the wrap makes can be very noticeable. 

Unfortunately, I don't think there is a clear "this one is always better".  Like many things, which one will be best for you is going to depend on what sound you like, your individual instrument, how you play, etc.  But if you are asking if it makes enough of a difference to notice and if you try some different wraps or brands of string are you likely to find you like one better than another?  Very likely.  I feel it is a thing worth experimenting with, since it can make quite a difference.

Years ago, when I was a guitar noob, I asked about the silver and gold plated strings.  I was told it was mostly just a gimmick or an ego thing and that the plating would wear off so fast that it wasn't worth the bother of trying.  Many years later, because I saw a set on clearance, I bought a set of silver plated "silk and steel" acoustic guitar strings.  The sound difference was very noticeable, and the plating actually lasted for quite a while.  So I tried a set of gold plated strings.  Also very noticeable, but on my acoustic guitar, they were brighter than I liked.  To this day, I prefer the silver "silk and steel" (which is synthetic core wound strings and steel  unwound strings, much like many violin string sets) on that particular instrument and for the sound I want out of it.  So I had done the sensible noob thing and asked someone more experienced and got a totally incorrect answer.  Nobody is perfect, it happens sometimes. LOL

Moral of the story:  Don't assume anything is "just for looks" on a musical instrument until you try it and hear for yourself.  It is easy to assume that a "prestigious" material like gold or silver, or an "exotic" material like titanium or chromium are just being used as a "selling gimmick".  Probably true sometimes, but not as likely when it comes to things like strings.  Whether you will like it better, though, you only find out for sure by trying.

So far as how long any given string material lasts, I've used some silver wrapped violin strings and some aluminum wrapped, and while I expected the aluminum to wear out much faster, they don't seem to.  So I'm note sure if conclusion can be drawn there, with any certainty.  At least not within my limited experience with violin strings.