Based on actual facts about alcohol absorption, Roe men can drink the most. Granted like all things, there are exceptions to this rule. There may be Roe females who are exceptionally skilled at masking their level of inebriation. However, based off off body mass and fat %, I'd rank the ability to put down the drink as such:

Roe Men
Roe Women
Highlander Men
Highlander Women
Elezen Men
Elezen Women
Miquo'te Men
Miquo'te Women
Hyur Men
Hyru Women
Lala Men
Lala Women

Sorry Lala, you may be the root of all evil, but when it comes to getting wasted, you're a cheap date.

There are also factors that may contribute to one race seeming more drunk than another. For instance, if drinking in a basement bar, elezen may be at a disadvantage due to repeatedly walking into the support beams in the ceiling.