Well, this is simply analog stuff, in the case of a simple op amp. The slew rate is manipulated by providing 'frequency compensation' in this situation, to make the op amp behave in a more stable manner.
...So, the very existence of external compensation kind of hints at just how obsolete an op amp like the 308 is, because many high performance op amps tend to have their own
internal compensation. It's kind of like points and condenser in an old car engine distributor - you don't see that used with modern cars.
Long story short - with the 308 or OP07 - it's a single capacitor that 'puts guardrails' on the frequency response. TTBOMK, ProCo has always used a 30pF cap for the compensation cap (apparently, it was suggested on the 308's datasheet itself).
...Assuming the 308 does indeed have a lower slew rate than the OP07, and it's preferable (e.g. 'clearly sounds better'), you should be able to tweak the value of the compensation cap with the OP07 (by making it bigger), thereby making the slew rate identical to the 308's.
View attachment 855281 ...So, again assuming the 308 has a lower slew rate, and this is why we prefer it, the OP07 would probably have a line on the above graph that's just a little bit higher and to the left of the blue line. Also assuming that it's probably just a little bit higher of a slew rate, it probably would only require increasing the compensation cap slightly.
I've suggested to a few folks to try using a cap with a value between 33pF - 39pF, with their OP07 Rat. One or two have told me that it 'sounded better', but I think at least one person said they still preferred their 308 Rat. It's entirely possible that the compensation cap might have to be increased even more, but this is all trial and error stuff, since we aren't actually measuring anything.
Anyway, the above graph (which isn't mine, BTW, and can be found here -
https://www.electrosmash.com/proco-rat) simply and clearly illustrates how the compensation cap affects the slew rate/bandwidth.
Who knows? Maybe you could make either op amp sound 'more better still' by simply increasing the compensation cap to be a bit bigger than ProCo ever did.