My 200 amp panel is about 100 feet away from the connection to the tub. I was planning to run 6 x 3 wire using a 60 amp breaker and take that to a 60 amp GFCI about 25 feet from the tub. Given the length of wire run should I be going up to a # 4 wire to avoid voltage drop?

I am planning on refurbishing an older tub with a 240 volt heater and 120 volt pump.

voltage drops aren't a concern on runs under 100 feet. The additonal 25 feet would be minimal, maybe a half a volt. Don't worry about running the 4ga wire. use 6ga