There is no correct answer tho this, but I'll be good and write an answer rather than a comment (I also beleiove this question is far to broad).
I won't touch on Horitsu's answer of the psychological impacts of a portrait.
It all depends on your subject, tone of your image and personal preference, as the different vantage points can change peoples heights, stature etc and if they're looking down/up can stretch the skin below the neck where as if the heads down this skin isn't stretched (i can't remember the correct term) and depending on the subject can look fleshy and lose, and in some cases (me when I used to be obese for example) really pronounces a double chin.
Personally I like to shoot at eye height to avoid this (and to avoid looking up the subjects nose), but when I shoot full length female fashion (aka, most of the time now) I tend to shoot from the floor upwards as it makes the legs appear longer, and makes the subject in turn look more powerful.
Analyse pictures of other photographers you like, see how they've done it, give it a go and see what works best for you BUT it is a situation by situation photographers choice so there's not an answer.