Rumor has it that the 510 was an upgrade from the 503 and, along with the provision for a heated O2 sensor, has more robust circuitry in selected spots.

I pulled a 510 from an 84 and put it in place of the 503 that has performed just fine in our 83 (built 10/82) for over 21 years. Absolutely no difference that I can tell...works just fine without a heated O2 sensor.

Our 83 has VIN: YV1AX8847D1835044, so it looks like your sedan may have been a very late 83 model. Since even at that later build date it has a 503, this suggests that the 510 in your wagon was swapped in at some point. The presence of a black wire to pin 19 on the ECU is interesting! My 1983 wiring diagram (factory Green manual) does not even show a pin 19 in the diagrams displaying ECU connections. Pin 18 powers up the ECU via a Blue-Red wire from the fuel pump relay when the ignition is switched on, and pin 20 is the signal from the O2 sensor....but no pin 19 shown.

AFAIK, the exact same ECU was used in manuals and automatics.
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Bob (81-244GL B21F, 83-244DL B23F, 94-944 B230FD; plus grocery-getter Dodge minivan, MGB, and numerous old motorcycles)

The 503 is the correct ECU for '83.

The 510 is proper for a late '84 that came with a 3-wire o2 sensor. Why it's in your '83, I can not say.

Can't say about internal differences, but both Bosch numbers cross to CU-91X, which is the ECU - Exchange # for '83, '84. (From 1992 Bosch catalog)
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Bruce Young,
'93 940-NA (current) — 240s (one V8) — 140s — 122s — since '63.