If you have a friend who can fly your railjack, then I'd recommend testing the gunner weapons yourself. Having crewed a lot of Railjacks as a gunner I'll share my opinion on the side turrets.
Apoc - Nice rapid fire cannons. Long range, gets good damage relatively quickly. Satisfying to use.
Carcinox - Nice rapid fire cannons. Long range, gets good damage relatively quickly. Good satus effects. Satisfying to use.
Crypohons - Very effective, though need to be used at really, really close range, and do need some skill on your gunners part to use as they kind of need to be fired instinctively.
Photor - Long range and hitscan are a positive, but the low damage so takes ages to get any useful amount of damage on a target especially if your using Zetki ones as your having to stop to allow them to cool. I find them awkward to use as a gunner due to needing to have to constantly re-adjust the aim as the railjack moves. I'll usually resort to firing missiles as the gun cools (if the Railjack is carrying a Tycho Seeker).
Pulsar - I just really don't get on with this one and will try find another crew position to fill instead.
Personally I went for a Carcinox on mine due to the stus procs. I'd look to use the non-zetki weapons on the turrets, just because of the extra heat buildup on the Zetkis.