OK lets add it up for Dorset
Record potential:
Grayling, Chub (and possibly minnow!)
Nationally significant:
Barbel, roach, dace
Big:
Pike (30+), perch (4+), eels (6+)
Nothing special:
Tench, carp, bream
Doesn't sound so bad, and I know of a lake near Hamworthy with double figure tench.
And just for balance, I used to drive for an hour and a half to get to Yorkshire from the lake district, where, in those days apart from pike and perch there really weren't many coarse fish of any size.
Having lived in Dorset (5 years) and Hampshire (7 years) I would say that Hampshire has the edge, but in my opinion they are both near the top of the big fish per squre mile league, and having grown up in the North I agree that, in general, you have to travel further if you want to catch a specimen.