All SDRs use DSP, so I think you are asking which SDRs have a dedicated DSP chip. Most low-cost SDRs don't.
Direct sampling SDRs need an ADC and some way to convert the digitized data into a lower bandwidth data stream that gets sent to a PC via USB or Ethernet. This is typically done with an FPGA and a microcontroller that supports USB. High-end SDRs have more expensive hardware than cheap ones. The cheapest ones often use an ASIC that was intended for some other application, such as a TV tuner.
I don't think there's an easy way to correlate performance to the presence or absence of an FPGA or DSP chip. Performance depends on a lot of things including the RF front-end of the receiver.