Which is better for an aluminum barrel nut - AeroShell 33MS Mil Spec Armorer's Grease or anti-seize ?

I would personally go with AeroShell.

AeroShell.

Some anti-seize has graphite in it.

I agree, I would use Permatex 77134 that is labelled as nickel based - typical use is for spark plugs.
This is the first time I will be using an aluminum barrel nut - always used Aero shell for past builds with steel barrel nuts.

Interesting thought about using antiseize. I would imagine it would do fine with the temperatures involved and that it is designed for an Al to steel connection.

I've used lithium grease with Al barrel nuts and they came apart without issue. One loosened up when I only used about 30 ft/lb torque to time it with the gas tube. It got re-torqued to 80lb/ft and eventually replaced with a steel nut when the rail was changed out with a lighter profile. The Al nut came with a cheap CN rail from ebay and the metallurgy/machining was likely crap.

The expansion coefficient of Al is almost twice that of steel. I originally thought it would be a good thing to have the same material for the expansion rates, but after experiencing that Al nut loosening up I've changed my mind. A steel barrel nut won't expand as fast as Al and will have a tighter fit as the barrel heats up.

If it were me, I'd just use the Aeroshell and check once in awhile to make sure it hasn't loosened up.