I've done some rubber mould making and hobby casting, but not pen blank casting. Having read all I can, this is what I've found.
Vacuum is used to degass the resin, either before adding catalyst and mixing, or immediatley after. As the bubbles of air form the resin can foam 2-3 times it's volume. Like opening a fizzy drink.
Pressure will initially shrink the air bubbles and then they will actually dissolve into the resin. Once the resin sets the air becomes trapped (dissolved) in the resin. Again fizzy drink, you don't see all the bubbles when the bottle is unopened because the pressure keeps the gas dissolved. Once you open the bottle (release the pressure) all the bubbles appear.
It's all part of the same coin. Lowering the pressure will release any gas that is already dissolved in a liquid. Increasing the pressure will cause any gas to dissolve into a liquid.
Heating the resin helps because the air can't dissolve as well, heat the air and the bubbles become bigger. Also a thick resin will thin out a bit letting the air escape more easily. The reason you see water boiling is that the heat drives out all the dissolved air. First you get a lot of large bubbles and then smaller and smaller until there is no air in solution.
Vibration/ultrasonics literally shakes the air out by producing alternating high and low pressure waves in the liquid.
I'd say that either vacuum or pressure will work equally well, provided that the resin doesn't set before all the bubbles have escaped/dissolved. I think that pressure is more common, as most people will have a shop compressor but not a vacuum pump. Also pressure won't make the resin foam and empty from the mould.