I find the liquid test strips to be more accurate (although they're far from perfect).
The frequency of testing is probably determined by what's happening with your tank. If it's a stable tank (it's cycled, your stocking levels are set and your fish are full grown), you probably only need to test your nitrates and do it a few times at different times in relation to your water change schedule to ensure you're keeping the levels under control (i.e. < 20 ppm) and to better understand how often you need to do water changes (and how large they need to be). After that you'd probably only want to test if anything seems like it's not right with your fish or tank (fish acting strange, dying or water getting cloudy, etc.).