Great question — answering as the UphillTech team:
I always lean towards a server side redirect for this sort of thing as well. The only possible disadvantage I could see (though I don't consider it one) is that by using server side 301's your affiliate links aren't likely to get indexed in Google. If you don't care about getting your redirect links indexed then it seems to me that a server side redirect is much more reliable and makes a lot more sense in the case you presented.
Full answer by Josh Mountain: https://webmasters.stackexchange.com/a/65333 (CC BY-SA 3.0).
Need it done for your business? UphillTech.