In online games, suppression rarely works because in most game modes there is no real penalty to dying other than your opponent getting a point. Its usually more worthwhile to to try and take the shot anyway, even under fire, as you aren't really losing much in the long run.
In a more realistic game, RoF is arguably more useful. They both translate into DPS, and since realistic games usually have realistic damage rates most bullet calibers will end up doing similar amounts of damage at the end of the day. And the ability to put more fire more quickly on a position will typically equate to more kills, as is the principle theory behind LMGs and SMGs.
But since suppression isn't effective in most games, I prefer damage. Its usually the most direct factor involved in killing an opponent quickly. There is typically a trade-off involved, like a low rate of fire or short range, but those can be worked around.
Take TF2, for example. The highest RoF guns are the Minigun, the Sniper's SMG, and the pistols. However, the SMG and the Pistols do such little damage that even a high RoF they still don't end up doing much damage. The Minigun gets the best of both worlds because its major weakness is mobility, but even it can't do any meaningful suppression at long range. Compare them to Sniper Rifle, the Rocket Launcher, or the Sticky Bombs. All very high damage weapons. They have low RoF, and involve more work to get good results, but are much more efficient at killing people at most ranges.