Well this all depends on what alt coins you want to store. As far as I'm aware both only offer limited support of only a few alt coins.

Here's a list of ones the Ledger supports https://www.ledgerwallet.com/cryptocurrencies

And Trezor https://doc.satoshilabs.com/trezor-faq/overview.html#which-coins-are-currently-supported

More than I expected but what one you should go for will depend on what coins you have or plan to hold. If you're going to buy one I'd wait until the new year as they will almost certainly have a January sale on.