The posts I've taken out have broken off at the top of the concrete they are setting in, so it's been tough.
I've found the easiest (none of it is easy) way is to dig a circle around the concrete, down about 4". Then wrap a chain around the concrete, hook it over a handyman jack that's sitting on a 2x6, and start jacking.
It only takes about six hands and four tries to get a good bite to jack it out.
Alternately, when I've been mad at my son, I send him out with a shovel and six ft long 2" shaft type pry bar and tell him not to come back until it's out.
After either of these, I have to use a concrete tube for the new post; the top of the hole is sometimes 18" in diameter.
Hope this helps.
ron