Magento 2.2.1 contains many more bug fixes, is a more up-to-date version of Magento and of course contains all the security fixes that are also present in 2.1.10.
If possible, you should always upgrade to the latest version. However, because 2.2 is such a big jump, this might not always be possible. In my instance, one extension that I'm using does not support 2.2 yet, and Composer complains about version constraints — I have no choice but to wait and to upgrade to 2.1.10 instead.
Apart from that, 2.2 needs a lot of testing, especially if you have a very customised instance. For more information about all the changes in 2.2, check out the official 2.2 release notes, and 2.2.1 release notes.