I was thinking "the same cabinet". Trying to decide if I should get a cab more matched to the lower wattage I may end up running into it...or if I should plan ahead and get a cab with more power-handling, that I might "grow into"?
Part of the trick on getting a cab that will handle both ranges of power is "how sensitive is the cab". How much power does it take to bring it to gig volume? The more sensitive the cab is, the less power it takes. HOWEVER, very often, but not always, the higher the power handling the cab has, the less sensitive the cab is.
Eden for example makes both XLT and XST cabs. The XLT cabs have a built-in low mid hump that makes them sound really good in a mix, but they don't handle as much power as the XST cabs and they don't go as low in their frequency response as the XST. The XST cabs have a very flat frequency response and also have a lower and tighter bottom end. They handle considerably more power than the XLT's do, but they are not as sensitive - not a huge difference in sensitivity actually, but nonetheless a difference.
And NOW, just to muddle your brain a bit more, there is no real standard of how to measure sensitivity. SPL ratings are typically done with an SPL (Sound Pressure Level) rating measured @1W1M (1-watt, 1-meter). That sounds pretty straightforward until you ask, "wait a minute, what frequency are they using to check that?" The frequency or frequencies used to check that SPL are very rarely quoted. From what I can ascertain, 1KHz is pretty commonly used. But what about the other frequencies? I don't only play 1KHz sounds?
About the only manufacturer I know of that tests and publishes SPL at different frequencies, plus an average of those frequencies, is Mesa and that's thanks to
@agedhorse. So when you see an SPL rating on his cabs, you can believe it. You'll often see higher SPL ratings on other brands that are actually not as sensitive in "real world" conditions. I'm an Endorsing Artist for DNA products and even when David owned Eden he didn't like the pick one frequency and issue an SPL, but he felt he had to do that because his competitors were. He also didn't feel it was a good metric to use. But you know, if you can't demo the cab yourself, how will know what it can do?
So now with his DNA speaker cabs, David publishes their power handling along with the max SPL instead of a sensitivity rating, feeling that is probably a more relevant metric. Until manufacturers start using real world multiple frequency SPL tests like Mesa does, this seems pretty good to me. And of course I have a couple of DNA cabs and I can just say, they are very sensitive taking very little power to play at giggable levels. But I've gigged with them a lot and I know from experience how they sound and what they can do.
So perhaps a better question would be what cab will handle my 600-watt amp when I need it and still be driven to giggable levels for smaller venues with my 300-watt amp. If you have experience with a certain brand of cabs, then you can look at their power handling and their published SPL rating and be fairly confident you understand what's happening. Presuming they don't change their SPL testing parameters from cab to cab, basing what you know of a cab you already have, you can get a good idea and make a decision from there. Still nothing beats trying out the cab with both your amps before you buy it.
It's not a problem to use a lower powered amp in speakers that can handle twice of what that amp can do. The problem you might run into is using the 300-watt amp in a venue when you should be using your 600-watt amp and you run the master so high or run so much boost in the EQ section of your 300-watt amp that you cause the power section to clip. If the power section is clipping very much, besides sounding crappy, that will (should) trigger your protection circuits and it will turn everything off inside (lights are on but nobody is home). So, make smart choices on which amp to use where.