When it comes to gear inches, does the chainring/cog size matter? For example, ratios of 51/17, 48/16 and 45/15 all have 81 gear inches (using 27 for wheel size). Will each of these feel the same? And is there any such benefit to having a particular chainring/cog size?

The only thing that matters is gear ratio = chainring teeth / cog teeth.

^so you're saying if the cog and chainring produce a particular ratio (3 for example), then nothing else matters?

The only other factor is tire diameter.

Efficiency. See the study beginning on page three.

There are some slight things to consider: https://sheldonbrown.com/fixed.html#gearing

Scroll down a little to "Big or Small?"

If two gear combinations (chain ring A and cog A vs chain ring B and cog B) produce the same number of gear inches, the gear combination that has the greatest number of teeth will have a tiny, theoretical advantage in efficiency.

The gear combination with the greatest number of teeth (with chain) will also weigh more, everything else equal.

Personally, I pick gear combinations with a prime number cog and an end result of 63 gear inches in mind.

For me, 45 X 19 with 28mm tires gives me my ideal of 63 gear inches:

https://software.bareknucklebrigade.c...it.applet.html