There's only a difference of 5 or 6 stat points between the best and worst race for any specific stat. So no, it's not going to be game breaking at end game. Pick the race that's most aesthetically pleasing for you.

Also, there's no limit to how many dungeons you can do in a day. As a tank you can literally just keep queuing up for them after you finish them and chain them to your heart's content.