I have the Black 1TB drive myself with a steam install on it,I've not benchmarked drive speed but it feels very snappy,for a games drive personally I think the extra speed of the Black would be beneficial.
The Green has lower power requirements and is possibly quieter but tbh i've never considered the Black to be loud,GB per £ is obviously a big consideration,do you really need 4TB of storage though?
Less storage,more speed all day long for me,lets face it 2TB is still a significant amount for a steam install,more than enough tbh even for the most prolific gamer.