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I'd say whatever the casing is made of makes a bigger difference. A cotton cased tyre definitely feels more comfortable than a vulcanized ones.
Vittoria or Veloflex Corsas and Specialized Turbo Cottons are both cotton case tyres which are very comfy. They also happen to have a high TPI.
Latex tubes are another way to add more comfort without having a bigger tyre and again add a noticeable difference.
Is there any merit to higher TPI tyres giving a 'plusher' ride? I'm on an old frameset, and don't have the room to go above 25/26c, but, do get rattled about a bit which I'm realising is putting me off riding.