Range is dictated by BB weight, hop and power - that's joules rather than fps.
BBs are generally the most stable flying between 280 and 320fps, this isn't something I can prove, it's just something I've noticed through experience (I've been playing around 7 years).
So to get the most out of your gun, you want to be using the heaviest ammo you can that will give you an fps reading in that bracket, whilst still being light enough for your hop to actually send it flying level, of course.
Why heavy ammo? The added weight makes it less susceptible to air resistance, it might start off slower than a lighter bb but it'll maintain its speed for a longer period of time. To the point where beyond a certain range it will actually be travelling faster than the lighter bb that set off going faster, just because the lighter faster shot will decelerate at a higher rate.
The other thing about heavier ammo, is that it retains the spin applied by hop for longer, making it actually maintain it's lift for longer. So even though it's heavier and you'd expect it to be more prone to the effects of gravity, that's actually not the case because it spins for longer and actually fights gravity for longer.
How does that make any sense? Well the hop rubber is basically a brake, right? It's a brake applied to only the top side of the BB, the more hop you apply the more harshly that one side of the BB is slowed down, thus the greater the spin - we all know how hop works.
But for a heavier shot, more hop is required to maintain the same - level - flight, so it gets more spin added, and that's precisely why it maintains the spin longer, because it's spinning faster in the first place.
So when people say fps doesn't give more range, they're not necessarily wrong, but it'd help if they clarified by saying that JUST more fps doesn't give more range. If you just stick a bigger spring into a gun and run the same ammo through it, the shot won't fly with much stability, the air resistance will just slow the shot down faster, and you'll probably end up with so little extra range that it just won't have been worth it. Especially once you consider the negative effects of adding a heavier spring will have had on the gearbox - more stress on the gears, the motor, your trigger response and rate of fire are going to suffer, and for what?
But, if you up the power via the spring, and then also increase the weight of the BB - ideally to drop the fps back down to what you were shooting at before with the lighter weight, you will hands down, 100% of the time see a range increase.
The thing that people get hung up on, is that they don't understand why you'd increase the fps only to decrease it again with heavier ammo. They feel like they've taken a step forward only to take the same step back, but it's not the case because bb weight is everything.
A .2 travelling 300fps will not travel as far as a .25 travelling the same speed. So a .46 travelling 300fps? Range for days.
Why'd you think sniper's use heavy ammo? It's all physics.