The DSP/processing technology is generally shared among the same line of products (i.e. all Marantz AVR receivers and AV processors will generally have the exact same DSP/firmware and possibly the same DSP boards).
However, the processors will be better because of these reasons:
1. Processors have significantly better power supplies for all DAC and analog sections (the basically equates to sound quality).
2. Processors will generally have balanced XLR outputs (this can be a big jump in sound quality as the XLR analog output boards can sometimes have a lot put into them).
In an AVR receiver, the DAC/analog power supplies are typically compromised or reduced (sometimes even chained off the main amp power supply). The XLR boards are removed in place of the amplifier boards and speaker connections.
I believe the DSP logic is the same between Denon and Marantz (they are both owned by Harmon and use the same DSP engineering team). The DSP boards may even be similar. However the DAC and analog audio boards are completely different between Denon/Marantz (the two products are voiced completely differently). Yamaha is a completely separate company and do not share anything with Denon/Marantz.
Some manufacturers may use the same chassis/case for both their AV receivers and processors. Anthem and Arcam are two examples. The Arcam may preserve the high end analog power supplies, but lose the XLR output boards (the Arcam processors are basically half-empty inside). I’m not sure on the Anthem because pictures do not show the bottom power supply boards on the receivers.