Great references both, for different reasons. First off, I think it is essential to point out that both these references will be discontinued shortly (both within 2019/2020)*. So, make your move!
The 5980/1AR will hold better in time (both aesthetically and monetery). So, my choice, right now, would be for this one. In addition, i think service cost difference between the two is going to be negligible, but call PP and ask.
The 5960 was a superb reference for Patek overall. The G should be the final itteration - and it is not the best one for sure. It is a watch I would consider, as a 3rd PP timepiece. Not the first, not the second. It is not an aesthetic result that you associate immidiately with Patek, due mainly to the color combination on the dial. So, it would be my third watch from Patek - to have something different, slightly off the core aesthetic route and to have some fun. Same logic as the 5524 and 5968 - other "3rd" Patek Philippe timepieces.
Whichever is your choice though, don't forget the most important factor of all. Enjoy it!
Cheers!
*The discontinuation argument is a personal guess. There is nothing official about this assumption.