Charcoal is better than propane, no question.
Oh, you mean "grille"? Why didn't you say so?
I actually don't even have the grilles for my Infinity Renaissance 90 speakers - it's unfortunate because they're actually integral to the speaker design. The grilles are shaped to optimize (reduce) diffraction off the front of the speaker. They're an unusual design, however, made of a solid sheet of MDF with holes cut out for the drivers - the drivers actually stick out of the front of the speaker cabinet so they lay flush with the surface of the grille.
As for the fabric - it should be acoustically transparent but I have no idea how that actually transpires. I can imagine that cheaper speakers may skimp on fabric, which may have a very slight attenuation of high frequencies. You could measure it easily, if it's large enough to make an audible difference. Grille fabric is thin though, so it won't have any effect on lower frequencies.
However, the effect of the grille frame may be larger than the fabric - as with the Renaissance 90, it could have either a positive or negative effect on diffraction.
As far as differences go - I would not rule out the psychological effect of seeing the drivers and knowing that there is "nothing between you and the music". That perception may well increase the apparent transparency of the speakers.