It can also depend on which TV is being used and whether the box or the TV is doing the up-scaling etc. Most TV come with default settings more suited to shop demonstrations rather than a real world living room environment and just adjusting the TVs settings can make a big difference - usually by turning OFF (or at least toning down) the manufactures features that claim to give a better picture quality.
Consider also that the broadcasters are trying to squeeze more and more content into the same bandwidth and on most of the lesser TV channels the picture is so filtered and compressed that no amount of processing in the receiver is going to restore the quality back to the picture. A lot of picture processing in these boxes is performed in hardware so the speed of the processor is more likely to effect how long it takes to change channels, search for timer programs etc. rather than effecting broadcast picture quality.