What size would be appropriate for me? I'm 173 cm or 5 feet 8.11 inches tall. The frame sizes I'm getting are 16 inch or 17.5 inch

Don't be confused by bike size - the 16-17 inch measurement is a measurement of the bike frame - from the center of the bottom bracket to the top of the seat tube. If your choice is mountain bike, that size sounds close. At your height, according to the charts I saw, you're probably closer to 17-18 than 16-17.

There are a bunch of bike sizing tables on the Net. Personally, I've always preferred a slightly larger bike when given that kind of choice, but it's really a matter of personal comfort.

As the other answer already mentioned there is no definitive answer to your question, as it is based on personal preference.

The only way to find out what works best for you would be to visit a local dealer / shop that has both sizes of the desired bike in stock. Take both for a testdrive and see for yourself what works best for you.

Second best option would be to find a shop, or a friend, that has one of the sizes and take that for a testdrive. See if you feel comfortable enough on that framesize to be wanting to make a purchase.