There are several things effecting quality.
Screen.
In most cases size for size, CRT is better than LCD. I saw Freeview running (Sky News channel) on a LCD last weekend and was rather shocked at the blocking lego effects around the text on the Sky ticker tape at the bottom of the screen. My 7 1/2 year old Sony CRT doesnt have any such lego effects around the same text via a Freeview box. Further, some LCD tv's are better than others. Some show up problems more than others.
Broadcast system (Freeview or satellite).
Both are digital, so we are dealing with compressed images. Satellite has more frequency capacity, which allows for more channels, but it doesnt always translate into a better picture (which is what a lot of sales people will try and tell you). The fact is that channel operators like ITV are not allowed to use all of that capacity - the operators pay to use X % of the capacity. So ITV dont have access to all the capacity, only a limited part of it, and the same goes for other operators, so Sky Sports for example usually looks good thanks to a large capacity set aside for that operation. This leads to some channels looking better than others, even though both are on satellite. With Freeview, there is less frequency capacity to share out, and its more or less full, so channels are operating close to the limits most of the time. BBC on Freeview have fixed capacity, while all the others on freeview share the remaining space. So in theory, BBC stuff on Freevierw should always look the best. With the other channels, the amount of capacity used varies depending on whats on screen and the free capacity has to be shared with the other non-BBC operators.
Source material/post processing.
This is the stage, beyond our control which is made of from the original content + any editing that is done just before broadcast. This will apply to satellite and Freeview the same. Poor quality ancient pictures stored on old studio tapes dont translate well into digital. Plus, any editing or filters added can make a difference - the last major football event showed that the BBC did it right, while the ITV coverage was plain bad.
The digital decoder.
The decoders used in either external digital adaptors, or those built into other equipment such as idtv's or freeview-dvd recorders, vary in quality. As has been well indicated on this web site, this can often make a difference in the signal reception - eg, how likely the box will suffer from interference, or how well it copes with a weaker than expected signal. But it goes further than that. The picture processing can also vary. Some decoders do produce a better image than others.
Dave