Southampton is a resort (golf, beach, etc.). The Princess is in the city. Both are very nice in terms of room amentities and quality of service, etc. I have found the Princess rooms to be on the small side whereas, based on a sample size of 1, the room I had in Southampton was enormous.
Location: from the Princess you can walk to a number of shops and restaurants. IIRC, it would likely require a cab to reach even the nearest restaruant to the Southampton.
There may be a shuttle available between the two properties, or a chance to do a two-property stay on the same trip.
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13F