Is it worth me upgrading the iPhone 4S to a 5S?

I would like to know everything that the 5S has to offer compared to the 4S and if it is worth me upgrading?

I currently have a black 4S 16GB which I purchased in 2011 and I'm keen on the white & silver 5S.

Yes definitely. From the 4s to the 5s is a big step, there has been a lot of changes since then. Also adding that the iPhone 5s is one of the fastest phones out there. Here is a comparison between both phones

Huge step first of all you get the bigger screen brand new design and plus you get huge internal upgrades as well you will definitely notice your phone will be snappier and it will run better with iOS 7 I would say yes upgrade you will be happy with it.