The difference would be as much as the % tooth difference. A 32T would give you a 6.6% lower gear and a 34T would give a 13% lower gear. I expect the 34T would be needed to give a noticable improvement.
One comment, an 11x48 is a very high top gear (118 gear-inches assuming 700c wheels). Do you really need that tall a top gear? As long as you are changing cassettes would a 12x34 do as well?
You will have to lengthen the chain by 2 half-links (i.e. 1") if you go from a 30T to a 34T unless the chain is currently too long, which I doubt. BTW, if you are changing to a new cassette, you should probably fit a new chain also unless the current cassette and chain are very new (say under 1000 miles).
Shimano cassettes are fine. I don't know if they are much more durable than SRAM but they are certainly as good. You will do well with either brand.