High performance DSP radios have crystal or other type of hardware filtering before the DSP to improve performance. This is to make sure the A to D converter is not overloaded and run to the rails or out of bits from large out of band signals.
IF DSP in itself does not always mean good or great performance, I've had some IF DSP radios that were grim due to poor implementation of the signal processing. I've had others that performed ok but the actual IF BW was nowhere near what what was selected. Bottom line is the radio mfr has to do a good job on the hardware front end, mixer and the DSP to equal a good or great performing radio.
One example of this is the Tentec Jupiter/Paragon where you could select a 1KHz DSP IF filter for SSB but you still hear high frequency sibilance in the voices, which means its still passing signals at least a few KHz wide. Other radios like the Harris RF-5000 series are like a brick wall where you can have massive interference at the edge of the receiver passband and you select the next narrower IF filter and the interference is completely gone. I also have a Tentec Omni VII which is a very good performing DSP radio, a Tentec Eagle which is a really really good performing DSP radio and both the Elecraft K3 and KX3 which are both top notch in performance.
Another example of not so good DSP is comparing the old Icom IC-706MKIIG to its replacement, the IF IC-7000. The 706 was a good performer, not great but good. The 7000 offered full DSP IF with lots of different BW selections but its ultimate performance falls way below the 706 series in ultimate receiver performance. I know lots of people who supposedly upgraded from a 706 to a 7000 and then wanted their 706's back when they discovered performance went backward. The 7000 problems show up mostly when the radio is on a large antenna and the receiver gets subjected to strong signals and usually not in a mobile setup.
So choose your radio wisely and based some on specs, some on reviews and some on real life experience. You can't go wrong with a radio in the top dozen or so on Rob Sherwood's list since you can't get there without some great performance, but also get a radio that you can live with which includes functions, layout and a sound that suits you.
prcguy