Mode S Transponders - Can ATC tell the difference?

I am the proud owner of a new $5000.00 mode S transponder. I just took my
first long trip with it, and I began to wonder if ATC sees any difference on
their radar screen with Mode S. As you know, Mode S transmits your aircraft
ID as well as your assigned code and altitude.

I did notice that Flight Watch (122.0) knew exactly where I was when I
consulted them - rather frequently due to lousy weather. When I told FSS I
was "about 50 north of SBY", to my surprise he said, "actually, I show you
34 miles north of SBY!". I have never had FSS be so precise before, and
this seemed to be true a couple of other times as well - they knew where I
was without telling them.

I was always flying IFR, however, so maybe I was just "in the system".

SO-O-O...

Does anybody out there know if Mode S appears different on ATC or FSS radar
or if they can't normally tell Mode S from Mode C? I would really like to
hear from a current FAA specialist familiar with current equipment.

Thanks,

DB