I would totally get a Rolex over a birkin, especially since you already have some. However your postings seem to want us to say get the Nixon and a birkin, so i will tell you Nixon and birkin. You can try out the fun watch and then decide if you want the classic.
My first instinct was to say get the Rolex!!!! But maybe you should get a cheap gold plated watch to see how you like having one on? Maybe a Fossil? You can get one for less than $100 and see if you like even wearing a watch or not! If you do, get the Rolex. You can always find a good preowned Birkin from a reseller. Or, keep the cheap watch and gets new Birkin!