My assumption that higher wattage would mean greater volume, all other things being the same

Generally this is true except for the following:

1) The whole point of more wattage isn't necessarily to have higher volume. It's so that you don't have to push your amplifier to the edge of its capacity when you want to listen to the music and a moderately loud volume. Having "power to spare" is a good thing even if you never play the music loud. It means that the music you play will be cleaner and less noise-prone even when playing at low to medium volumes.

2) Make sure you know the difference between RMS wattage and peak wattage. The RMS numbers are more accurate and should be used for all comparisons. Many manufacturers and catalogs will report peak numbers which are essentially meaningless and can't be used reliably for comparison. That's one reason I like Crutchfield, they always quote the RMS numbers.

A five-channel amp that puts out 25-75 watts RMS to the four main speakers, and about 100-200 watts RMS to a subwoofer is often fine for most folks, provided they have good and efficient speakers.