Most of the guitar students I get who have studied with someone else or on their own subscribe to the idea that it's an either/or situation. Truth is that it needs to be neither or both. In other words, thumb position depends not on an adopted style, but on playing requirements. Use your thumb to dampen the low string(s) or fret the sixth at the second fret for the D chord for example, which will enclose the neck more closely with your hand. Also use your thumb in the more traditional classical style for barre chords. Also, bring you thumb out front of the fingerboard when playing way beyond the edge of the guitar body. Letting your thumb dictate your style is restrictive. A fluid relaxed left hand position is liberating and releases the tension from the hand which increases dexterity and agility. Allowing the thumb to be positioned at approximately the centre of the neck usually means that strings can be fingered without accidentally touching (muting) a neighbouring string, and reduces the likelihood of cramping. I also prefer this positioning for single-note (lead) playing.Btw, when standing you still shouldn't cradle the neck as the guitar should be balanced from the strap, not on your hand.
Happy New Year, I'm staying in. Mooh.