It all depends on the situation I guess.
Wading on the ocean flats will make a belt pack submerge when crossing channels, in fact anything lower then the elbows will be submerged frequently. However I love the belt packs for summer river fishing in summer without waders, and have used one for many years. They swivel to the rear when not in use, and to the front when you need something. As Moose says no strain on the shoudlers.
A good chest pack puts negligible or no pressure on the shoulders due to the horizontal belt which suspends the weight off the vertical shoulder straps. It doubles as a light daypack in the back for lunches and spare spools, and the very best ones flap down on the front compartment to provide a work area for tying stuff or whatever. You can put a hydration unit in the back for summer flats fishing, a real plus.
I only wear vests when winter steelheading from the bank, and that's mostly from tradition and due to the fact that it's all set-up for river fishing. For instance the Simms vest with the inside pockets for the steelhead permit, the two long pockets for the wheatleys, and the other stuff like leaders. Fits perfectly under the Patagonia SST jacket in a spring freshet and does not kill the spey casting moves too bad.
I did use the chest pack for steelheading a couple times out and it did work out very well worn on the outside.
I do not like any of the ones on the market today although many are acceptable each has it's plusses and minuses for instance backpacks that are not removable.