Have your tile setter make a mockup board with the two grouts. NEVER make your final decision off of a sample board.

Avalanche is actually white. Eggshell is off white. Neither look good with white tile. You want Moonbeam or Frost, in UltracolorPlus FA, NOT standard sanded. Brick is really porous and needs to be sealed first, and the grout done via groutbag. It's going to absorb everything and be difficult to clean, no matter how much you seal it.

@Minardi We actually prefer white over off white. We are planning on sealing the brick after the grout is done so the grout can be sealed as well. Thank you!

@millworkman I’m making the sample boards myself to see what grout i like the best. Thank you!

@Beth H Do you know where to buy the Avalanche, Lowes doesnt carry it anymore. Thank you!

Simple Google search will show you dozens of places, both locally and online. Mapei Avalanche Grout

I have Avalanche in my guest bath for the shower surround. It looks very bright white to me, but I can’t speak to how it compares with the eggshell color.

jAvalanche is stark blinding white. It only goes with very stark bright white tile. Any of the more off white tiles or marbles look better with Moonbeam, Frost, or Warm Gray. It depends on the dominant background color of the tile.