The stats won't change from upgrading, but they will when rerolling them with P Skulls.
It is recommended to use Diadems only due to the ilvl.
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There are four different types of circlets:
Circlet (qlvl 24, magic_lvl 3)
Coronet (qlvl 52, magic_lvl 8)
Tiara (qlvl 70, magic_lvl 13)
Diadem (qlvl 86, magic_lvl 18)
Since these all have a magic_lvl, the alvl formula is simply:
alvl = max(ilvl, qlvl) + magic_lvl (capped at 99)
From this, we see that circlets always have alvl 27+, coronets always have alvl 60+, tiaras always have alvl 83+, and diadems always have alvl 99.
Or, put another way, the minimum ilvl you need to have alvl 90 (necessary for +2 skills) is 87 for circlets, 82 for coronets, and 77 for tiaras, while diadems will have it at any ilvl.
So use diadems. They'll always have a chance at +2 skills, no matter what the starting ilvl is, no matter what your clvl is, and no matter how often you reroll them. The same cannot be said of the others (if you have a very high clvl character and a very high ilvl tiara, you could reroll it once and still have a chance, but that's it).