Is your derailleur capable of a 28-tooth cassette? Not all are.

I always count on readjusting my derailleur whenever I change cassettes, even like for like, due to manufacturing tolerances.

It is likely that your B-screw adjustment needs to be changed when you change the cassette for one with different numbers of cog teeth; perhaps this is why the 27-tooth cassette ran OK but not the 28.

If you are going to put a larger cassette on you must be sure that your chain is long enough that you can comfortably shift to your large ring/large cog combination without straining anything. Test this while pedaling gently by hand.