What's the difference between Proceed's amplifiers

Specifically, the HPA3 vs. AMP3 and HPA2 vs AMP2.

Any insight would be great! Thanks.
The HPA2/3 are the more recent models, circa 1998.
The Amp 2/3 series dates to 1994.

I have a couple of Amp-2s and an Amp-3. I think the HP series are larger and have greater power. I have read that the HA series doesn't have quite the same sound, but I don't know that. The Amp-2 and Amp-3 are fine amps, with an excellent power band, and balanced inputs. Each channel has its own large tyroidal power transformer.

Is there a significant difference in sound quality?
There is a difference, how significant it would be is up to your ears/wallet to determine.

Why the curiousity about these particular amps? You do know that the Proceed line no longer exists don't you? Do you also know that Madrigal no longer owns/markets Proceed/Mark Levinson components? Harmon International owns them now. FWIW, I have heard that service can be an issue, are you aware of this?
I would think that unless someone was giving them away, I might be looking for another amp. There are many good ones out there, even on the used market.
I recently sent my Levinson amp in for service. It was turned around in about 3 weeks. I know that there was a time where service was an issue due to the transfer of ownership.

But in my experience - Harman did an excellent job servicing my old 336 amp (which sounds better than ever mind you). I wouldn't hesitate to buy a Proceed - I think they are a great value (especially the HPA series).

Just my 2 cents.
The HPA's have double the rated power at 250 watts @ 8ohms compared to the Bpa/Amp series at 125 watts @ 8 ohms.
Actually I believe the BPA are rated at 150 watts but they are about the same as the Amp series.

The HPA and BPA were newer than the Amp line.
With all due respect to Jmcgrogan2, the fact that the amps are out of production should have no bearing on your decision to purchase them.
Buying these amps puts you in the same boat as ANY amp that is out of warranty. You will have to pay for repairs no matter who made it. Any technician worth their salt can repair an amp. The only caveat to this is if certain transistors become obsolete. The Proceed does not have this issue (at least for now) but it is just as possible for ANY amp by ANY manufacturer to get into that situation.
And, as others have noted, Harman still supports the product line with respect to repairs AND warranty (if it is still under warranty). That being said, the Proceed amps are VERY reliable and I have owned two AMP 3's and an AMP 5 with no issues.
Kudos to you for recognizing a bargain when you see one.

Now, to your original question, the BPA series were more of an evolutionary update to the AMP series (yes, there were electrical changes but nothing earth shaking different in the sonics). The HPA series were the higher-power versions 250w vs 150w and reportedly, improved sonics over the AMP series (less dry).

I've read reports that the sonics of the HPA and BPA are not quite as transparent and clean as the Amp 2 and 3, but that may be another person's dry.

Having used an Amp 2 and Amp 3 for over a decade, I'd say they're reliable. I had a minor problem with the Amp 3 fixed locally and the comment came back about what a pleasure it was to work on such a beautifully made piece of equipment.

Last year I bought another Amp 2 to use with a spare PAV. The other Amp 2 and Amp 3 are used with a PAV/PDSD. The amps are used in balanced mode, and drive KEF Reference 104/2s and 102/2s.