Depends on your size - I wear small / medium (unlike the typical tubby TZUKer), and I find at this size, it's very unusual for a polo not to fit - even primark ones which I buy for cheap & chearful holiday wear.
Having said that, I really like Luke polos, and also Penguin (their Heritage slim fit are lovely, though you mention you prefer not to wear slim fits).
I find that the only difference in branded polos are the embellishments, colours and logos - in small / medium they pretty much all fit just the same.
EDIT - I hate the Ralph Lauren cut due to the really long tail at the back. I prefer them to be the same length all the way around.