Or the original Severn Rail Bridge, which has had 65 years of very literal downtime.
en.wikipedia.org
A bridge will need to be high enough to meet clearance requirements for Sharpness and Gloucester, as well as having a main span long enough for the biggest width of boat. I don't know whether the changes in marine traffic mean that could be kept lower than either Motorway bridge if sufficiently far upstream, but if it needs to be lifted clear then having an enclosed tube is going to give the wind a big flat surface to hit. Even wind baffles aren't 100% effective and would need maintenance.
On the flip side, the gradient in the tunnel to clear the bed of the estuary is essentially 1:100 downhill from Patchway down to the midpoint (although the normal downhill track has steeper points, due to being an older design), then 1:100 up from the Midpoint to Severn Tunnel Junction. You can certainly hear diesel trains working hard on the climb up from the tunnel to Pilning. A modern tunnel may be able to lessen the clearances required to the estuary floor and start from a different point to minimise gradients but there's a limit of what can practicably be done as the main navigation channel will need to be cleared.
There's no easy answer, unfortunately. A bridge upstream of the M48 somewhere would likely make the best economic case as it's more sheltered than out in the open estuary, is spanning a narrower part of the river, would have less intense gradients, would not need the same restrictions on 2 trains being in the tunnel at the same time for evacuation/train rescue purposes and is upstream of the main docks for the really big ships.