I have been riding a road bike for 2 years now and I am being forced to replace it due to damage. I am now considering upgrading to a 11-28T rear cassette. Would doing so give me a major advantage as opposed to a 14/28T cassette?
With 11 teeth, you'll get more range when you max out. However, the 14-28 cassette will feel smoother as you go through the gears, because the number of teeth of adjacent gears will be that much closer.
For my money, you spend little enough time in those highest gears that any "advantage" is debateable.
Like another answer pointed out, there will be a difference in how the transition between gears feels; assuming they have the same number of sprockets, shifting from one gear to another on the 14-28 should feel "smoother" than on the 11-28.
From a performance standpoint, the 11-28 will give you the option of more speed, by virtue of you having smaller sprockets available.
However, you asked whether these things are noticeable, to which I would say: it depends. Here's why:
If you are a commuting or more recreational cyclist, the answer is likely no. Many commuters don't spend much (or any) time near the bottom of the cassette. If you're more of that style of rider, you may only get to the bottom of the cassette during a steep descent. Many of the commuting cyclists I know have about as much use for 11t cassettes as they do 53t chainrings.
On the other hand, if you are a more of a competitive or racing cyclist, you will most likely be able to notice the addition of the smaller sprockets; both on descents and flats, depending on ability. Some of the racing cyclists I know regularly find themselves near the bottom of their cassettes, during hard efforts. If you're a racing or aspiring racing cyclist, you'll probably notice the advantages of the 11-28 cassette.