You do not mention what antennas your are using nor what bands you are interested in "upgrading." So there is no single answer to your question. Having said this, here are some thoughts on the subject.
Higher power amps are not really worth the resources needed, unless you really need a "quick fix" for more QSO's.
A practical reality is if you are using your 600 watt amp on an antenna with no gain and you switch to using an antenna with a modest 3 db gain, your signal at the receiver end is similar to what it would be if you changed from a 600 watt amp to a 1,200 watt amp.
In most cases, the change from a no-gain antenna to a 3db gain antenna costs less than a higher power amp. Quite a bit less.
But wait. The same applies it still want a better signal. Increase your 3db gain antenna to a 6db gain antenna and your signal at the receiver end will be the same signal as if you were running a 2,400 watt amp.
Better yet, antennas, in general are less costly than amps and require very little maintenance, when compared to a high powered amp.
That's not all. When you improve your antenna's transmitting gain you also improve the antenna to your receiver. It too, benefits from a better antenna -- and you can hear the weak ones better! This is not true when you just increase the power of your amp, no receiver gain there at all.
Finally, when practical for the band of interest, install an antenna with front to back gain, a yagi or quad, perhaps. The advantage, of course, is you can poke your signal in the direction of the guy at the other end. This makes both of you happier.
However, in the real world these formula's seem to sometimes work differently than expected.
For some reason the second most important of most ham's antenna system really isn't given a lot of thought -- the feed. Using available manufacturer specs for all parts of the feed, calculate the db LOSS of all the feed components, ALL of them, not just the coax. Include the adapters, the switches, the connectors -- everything. You will be surprised to discover the a chunk of your 600 watts is being "eaten" by the feed line from the amp to the antenna.
Suggestion: start with the feed line (use the best coax you can find) then check out the antenna. This where the on-half of the db value starts to really rear its head. Who knows, you might not even need an amp at all.
When I run an amp, which is seldom, it is a Collins 30L-1, the best overall value in an amp purchase on the planet. It will go on any HFband above 160M and will continue to increase in value if you maintain it properly.
Cheers,73's and good DXing...
AL
K4ICL