First, you won’t be disappointed, both nominal groups will be understood and you will have what you want.

Secondly, the main meanings behind those two words are :

• gros :

  • it will have the meaning of big
  • but also the meaning of huge girth and volume.
  • It may have even the meaning of fat.

• grand :

  • will have the meaning of tall,
  • large number
  • but also all that come with being tall, a bigger mass than a smaller one
  • and even a high quality meaning as the size of your achievements.

So, if you order “La plus grande bière” what you could possibly have :

• a huge beer (which is what you want)
• a high quality beer
• a regular beer served in a very tall fancy glass

and “La plus grosse bière” :

• a huge beer (same as above)
• a regular beer in a large girth glass

I must add that in my understanding (I am French) gros bring a more familiar meaning than grand.

grosse bière may be more suitable in a bar context (use your gourmand eyes when saying it) while grande may be more appropriate in a classy reception.

Neither are really idiomatic in France. Asking for the largest quantity regardless of the quality would be often frowned upon.

La plus grande bière might be understood as the greatest, the most famous one while la plus grosse bière seems just odd. La plus grosse/grande bouteille de bière (que vous avez) or le plus grand verre de bière (que vous avez) would be preferred.

One the other hand, une petite bière is much more common, and doesn’t mean the beer is specially small.

In any case, the size of a beer served at least in France is pretty standard, it is almost always a demi (originally half a pinte, now a quarter of a liter) and there is also the pinte (1/2 liter).

Bottled beers can be 0.375 liter.

Unlike in other countries like Belgium or Germany, larger glasses/bottles are very rarely served.