Depends what school of music you go to, basically.
But for me, that is trained the "russian piano school", I would argue that arpeggios work up the keyboard best with a "low / flat" wrist, and arpegiating down the keyboard works better with a wrist slightly tilted the way you hand is moving and somewhat positioned more upwards.
However, in a general case. Legato with the wrist down, staccato with the wrist up.
And if you are tense with a raised wrist (I am not), perhaps you need to work a little more on some relaxation techniques.
It's a daily struggle though, some tenseness won't hurt you. But it's not a bad thing acknowledging when you tense up, perhaps it's something other causing the issue when you raise the wrist. How high/low are you positioned on the stool, do you have a straight or bent back, where is your elbow positioned etc. It's a million things. But if it dosn't hurt you or cause you to faulter due to lack of stamina because you tense up, don't worry so much.