No one has mentioned the difference between ripping and crosscutting and which part of the cutter is doing the cross fibre cutting.
Assuming the same chain speed and degree of sharpness, the majority of the energy required to create a chip is the cutting thru or across wood fibres while less energy is required to scrape out the fibres. Just think of how hard it is to cut across the grain with a hand chisel compared to cutting parallel to the grain with a chisel.
When crosscutting the cutter corner and side plate cut thru/across fibres and the top plate scrapes out the fibres. The number of fibres cross cut per unit time directly determines the cutting speed.
When ripping, the cutter cutter corner and top plate cut thru/across fibres and the side plate scrapes. Now cross cutting more fibres using a wider chain has to make more sawdust without necessarily increasing cutting speed.
Using 3/8 or 404, cross cutting involves the same total amount of side plate or cross fibre cutting since both gauges have to cut the same depth or length of cut. Provided the powerhead has ample/sufficient power a 404 chain has an advantage because it has a longer side plate and can cut across more fibres with each pass and it has a bigger gullet so it can also clear the fibres it cuts. Sure it also has to scrape more fibres but much less energy is required for that process.
Ripping involves cross fibre cutting using the toplate. Hence, just to make the same length of cut a 404 has to cut across more fibres than a 3/8. That's why the powerhead has to provide more power to a 404 chain to maintain the same ripping cutting speed compared a 3/8. Sure the 404 can scrape out more fibres and less energry is required for that process but it has to cut thru the fibres first. The harder the wood the more obvious this will be. In smaller softwoods it probably does not matter and the difference will be marginal
With a stock 880 and 660 I cannot tell the difference between 3/8 and 404 when cross cutting but it does not surprise me that a 404 can be made faster on a powerful power head. When ripping in wide hard Aussie hardwoods on an 076 and 880 I find the 3/8 wins every time.
Then there's noodling which is different again since that involves toplate shallow angle cross cutting of fibres (the easiest of all three cuts). I'll leave that one for you to decide on