I reckon I've been over both sides in both directions, but as
@Soltydog says, there is usually only one path open.
If you do have a choice, I think there's not much between the views from either path.
Worth being careful as you pass the two main towers - the path narrows and zig-zags to get around them.
Fairly easy to smack one of the towers or an oncoming (faster) cyclist, particularly if you are busy admirin' of the view.
Again as Solty says, it's quite a pull from south to north until you reach the crown of the bridge.
Not steep, but relentless - you cannot get any momentum going even on an ebike.
Another point about climbing is that from most directions there's quite a pull up towards the bridge before you drop down to the cycle path entrances which are at estuary level, off Far Ings Road on the google maps link below.
As regards views of the bridge rather than from it, the best of these are from the south side.
@Grant Fondo's pic earlier in the thread was taken from somewhere near the Waters' Edge Country Park, which is beside the estuary close to the eastern side of the bridge.
Easy access to the park from the entrances to the bridge cycle paths.
The park has a decent cafe with a small outside deck over the wetlands, so is a pleasant place for some pre-bridge crossing refreshment.
But it is another of those establishments that doesn't serve hot food much past 2.30pm, and closes entirely about 4pm.
https://www.google.co.uk/maps/place/Waters'+Edge+Country+Park+&+Visitor+Centre/@53.6963464,-0.4437548,16.63z/data=!4m13!1m7!3m6!1s0x47d6208f7c0160ad:0x6d447e9d82f130ff!2sHull!3b1!8m2!3d53.7676236!4d-0.3274198!3m4!1s0x4878eae3968cdbb9:0x5fd10b4ecc751bc7!8m2!3d53.6969891!4d-0.4418537