Not all DSP radios mute, though. My Grundig G2 doesn't mute. My Sangean PR-D5 doesn't mute, my Sangean PR-D14 doesn't mute and my Sangean PR-D18 doesn't mute. I've found that DSP radios are better for DXing sometimes, and not better sometimes. It just depends on the radio and the propagation conditions. My G2 is better on SW than my analog radios most of the time.
On the AM band, it's a tossup. I prefer my analog radios for that, although sometimes my DSP radios outperform the analog ones.
I think with the analog tuned DSP radios, you have to really fine tune them. My Radio Shack Pocket Radio is an analog tuned DSP, and it's easy to tune it too far to the right, or to the left, and miss a station. And that radio is the one DSP radio I have that has some muting. It still works OK with an external loop antenna, though, which helps to defeat at least some of the muting.