This is a better question, and comparing 318 vs 360 and 360 vs 408 is the right approach because the engines are all limited by what can be put on top, either by budget or availability. It's not like we can go out and buy aluminum W2 heads ready to bolt on. The only good offset heads out there require someone well steeped in the knowledge of those heads and what-works-with-what, and comes at a hefty price tag too.
The original question of 'does CID always make more power' is far more open ended and impossible to state 'no' to.
So, with that in mind, and the better question from above the answer is absolutely nothing. The only reason I opted for a 408 over a 360 is that the cost difference in the shortblock was trivial - so bigger is better, right? If I did it over again, the only thing I'd probably do different is A) not kill my original shortblock with stupidity and B) re-apply the money from the dummy-induced-rebuild into a monster top-end to let this sucker breathe, because every 408 with non-offset heads has asthma.
The rpm difference required of a 360 vs a 408 to make 'the same' (and I mean this relatively since the curves will be entirely different) power wouldn't be unreachable (408@5500 rpm is 1300 cfm, or a 360 at 6,233 rpm - a 360 at say 7500 would be 'equal' to a 408 at 6,600). Obviously this comes with some major caveats because the engines are going to shape their curves and change peaks due to other differences. But that said, it wouldn't be money wasted to put even better heads on the 408 short block. That way you can reduce the compression height of the piston vs trying to make heads and intakes fit a lowered deck. What heads? I couldn't even guess - which ones are the right ones for a big-inch small block seems to be a question best left to those who specialize in building them since most solutions require the right combination of parts, and it's not a magazine-build type of deal at that point.
But look how many guys on this very site are running in the 9's with stock stroke small blocks and many with stock (albeit modified in some ways) blocks. I wouldn't want to drive one on the highway, but they get it done and then some. With an overdrive swap, there's no reason the cars couldn't be street driven though - or close enough to street drivable for me!
The key to making the smaller engine compete with the bigger one is ensuring it's operation stays in the right rpm range - which is a matter of gearing. The same gearing that could make a street car less fun to take down the highway (anything 60mph and below though is still cake).