Quoted from benheck:
It can make a difference. The high power flippers on AMH peak around 5 amps, but going from a 7 amp to 14 amp switching supply gave us more "oompf"
Makes sense. Ignoring inductance... if your flipper coil has 4 Ohms impedance and you're running 48 V, it'll want to pull around 48V / 4 Ohms = 12 amps. If your supply can't supply that for the length of the pulse, you're losing power. I'd be surprised if you're current starved at 24V and higher impedance coils on BP, but it's simple math to ballpark it.
When considering inductance and charge times and such, things get more complicated. Ignoring the math, you're never going to get a great flipper snap with a 24V supply, but you could try more powerful coils (or taking a bunch of windings out of the coils it has now).