I think it would qualify as noticeable, although I had the change-out done before I even picked up the bike. From the math it is about an 8% reduction in the lowest gear ratio. Since the replaced cassette was unused, the charge for the swap was $30, which I thought was reasonable. Swapping out both the rear derailleur and cassette for the Ultegra 11-28 cassette would have been a fair amount more money, although I didn't really get a firm price.

The bike I was replacing is (I still have it) a 1980 Raleigh, which has a 52/42 crank, and an "Alpine gearing" 5-speed freewheel with 14-17-23-30-34 cogs. The lowest gear combo on the new bike (34/27) is very close to the lowest gear combo on the old bike (42/34). Actually, since the new bike has longer crank arms, and also weighs a lot less, it's a lot nicer on the hills than my old beast.

As an aside, on the Shimano web site they list the available cassettes for each group, and also the restrictions that apply to the various derailleur choices.