The simple answer is no.
Freeview and Freesat both provide the same core channel list as part of the Public Service Broadcasting remit. This is basically what the licence fee is about. Once you get past the core channels then there are some relatively minor differences in what's offered, but not enough for most people to completely bin one or the other.
FWIW, I've found Freesat to be marginally better picture quality than Freeview because it doesn't appear to be so heavily compressed. Also, you won't have to worry about retuning. Freeview is going through another round of channel shake-ups as the 700MHz band is being prepared for sale to the mobile phone operators.
The satellite tuner built in to your TV is designed to pick up from the Astra group of satellite transponders at 28.2 degrees east. This is basically Sky and Freesat. There are some channels in the group that don't appear on the regular Freesat EPG. These tend to be foreign language channels. Have a look at the
International subsection of the Astra channel listing
HERE These channels can be manually tuned with a Sky box. I'dd be surprised if your TV satellite tuner couldn't do the same.
There are more satellites up there whose transmission footprints cover some or all of the UK. However, to pick up from them you're definitely going to need an external tuner box and a second dish pointing in a different direction. These are mostly the European satellite channels:
Astra 1 at
19 degrees east (mostly German, some French and Spanish).
Eutelsat hotbird at
13 degrees east (Italian, Polish, French, Thai, Chinese, Arabic, Russian).
Atlantic bird 3 at
5 degrees west (only French free to air channels). Whether any of these are of some interest to you is your decision. There's a basic beginners guide
HERE
If you're looking to supplement what's available via Freesat without an ongoing monthly commitment for a full TV subscription then you might want to have a look at YouView.