The AD620 is smaller (8-pin) and cheaper $5-$10US at Digikey
The AD624 is larger (16-pin) more expensive $30-$50US at Digikey
The AD624 has pin-selectable precision gain, but since absolute amplitude accuracy is not very important in ECG, I don't think this much needed.
I have not used either one, so that is just my take from the datasheets.