Hammer spring tension manipulates energy, which translates to valve lift (how far the valve opens).
Hammer throw manipulates momentum, which translates to valve dwell (how long the valve stays open).
Granted lift and dwell are like horsepower and torque...you can't have one without the other. It's just that spring tension does more to influence lift, while throw does more to influence dwell. The reasons are easier to understand if we consult the equations for each.
Energy: E = 0.5mv^2 <- Notice the velocity term is squared. High hammer spring tension accelerates the hammer better and helps it achieve a higher velocity. And since we square the velocity, it means we get a disproportionate increase in energy which means more lift.
Momentum: p = mv <- No squared terms this time. Both mass and velocity have an equal influence. Our hammer weighs whatever our hammer weighs, but if we give it a longer runway, it will achieve a higher velocity and therefore generate more momentum which means longer dwell.
So which one is preferred in what circumstances? Well, it depends on what you are trying to achieve. As dizzums says, if you can set it up so there's just a smidge of hammer free play (e.g. 1 to 1.5mm), that will help prevent air-wasting hammer bounce. To be most effective, you need either a short, stiff spring with zero preload or an SSG to apply preload to a softer spring and capture it so it isn't leaning on the valve stem. The idea being when the hammer rebounds off the valve stem and heads back toward the spring, it won't do so strongly enough to recompress the spring and send the hammer back at the valve stem with enough gusto to knock the valve open a second time.
Or if you are shooting super heavy pellets or slugs, you might want to maximize the hammer throw to get more valve dwell. Heavy projectiles take longer to accelerate down the barrel which means they benefit from the valve being open longer. Giving it more hammer spring tension will also do it, if you aren't butting up against the spring's limits (going coil bind). Or it may simply be that you don't want the added cocking effort that goes along with more hammer spring tension. For a given cocking effort, increasing hammer throw will give you more lift and dwell. Meanwhile, more throw means slightly longer lock time...the time between the sear breaking and the pellet leaving the barrel. That's not as much of a concern when shooting from a well supported position as it is shooting freehand or other bodily-supported position where you are swaying.
