Dimmers work by firing SCRs in a delayed manner, called "phase angle control" which just means each SCR is on only part of each sine wave cycle. The longer it is on, the more RMS voltage gets through to the load.
SCRs are not perfect conductors when they are on; they reject approx. 1-1/2 watts per load amp. So if your load is 585W in either case, the heat rejected by the SCRs is going to be the same regardless of what the dimmer is rated for. The rating just denotes the amount of power that it can safely handle without overheating. If you tried to pass 990W through the 600W dimmer, it's heat sinks could not move the heat away from the SCRs fast enough and they would let the magic smoke out. 9900W through the 1000W dimmer however is not going to do it any harm because it has more heat sink and maybe larger SCRs (maybe not actually).
