That's a tricky combination. I would say the gs (with a pair of decent tyres) is more inclined to do some off-road. Plus is a more recent machine with probably more accessories available. You also get some more power.
The overall construction of the inazuma in not really geared for off road. having said that, I did see someone fit it out for off-road with decent results. Plus, factory gearing will favor lower revs.
I can not tell you much in terms of off-road for the zuma. I do mostly highway at 70mph (95%) and occasionally venture into the city. The zuma behaves very well in both. My road tyres do a poor job on gravel and even worse in mud. Plus the clearance is not great and you have the oil filter in prime position to be hit from below. The forks and shock also are not designed for that neither.
From the pics I see of the gs 310, I would say that its got higher clearance and better angle of attack for off road, while it would probably do fine on the highway. Specs say its slightly lighter also.
There are other variables you might consider though: Total Cost of Ownership. You pay up front for the bike... but how about servicing? how about spares? any special tools needed? aftermarket options? The advantage of the zuma is that the motor is used in the gsx, gw and dl (have you looked at that one? dl250, not sure if they sell over there, little brother of dl650 v-strom https://www.globalsuzuki.com/motorcycle/products/v-strom250_a/
). Accessories for me here are a problem. Not many were sold and we never did get the 2017 model... so aliexpress is my goto.
I've had my zuma for 2 years, put 41k km on the clock. Ride almost every day. It has been a fantastic moto. Could not have picked a better first bike. Just right. I take good care of her, do all my own servicing. Best oil I can get, filters, sparks, chain etc...
Personally, I think you should decide clearly if you are going to like doing more off-road or not. If so, I would look into a dual-sport: if you take it on the road it will be fine and on the trail it will be fun to ride. If you take a commuter bike on the trail it will suffer...