We have had a TT since 1976 and we always travel with full FW tanks because some water on the road taste bad. We have plenty of truck so really can't tell any different in handling or fuel mileage.
...snip... Having full tank also allows us to use the toilet while on a long trip.
Our trip is under 4 hours and there are plenty toilets & food available. The RV is basically 'sealed' during transit. The tanks are reserved for boondocking.