Tests with provided answer choices restrict in-depth and out-of-bounds thinking. Never give a student a 25% chance of getting an answer right. Give them unlimited choices and unlimited opportunities That's the way students learn.
Then again, tests that aren't multiple choice or matching or fill-in-the-blank are super stressful on students. So, if you can, make sure your students actually understand the content before you shove a quiz into their face.
As a student, I know how hard it is to remember EVERYTHING you learn in a year, and then summer happens and you forget it all. You remove those tattoos your teachers drew into your brains and you look back on all of that wasted time. So don't test a student's memorization skills. Test her learning.