How does the decibel rating vary with the BTU capacity of an air conditioning unit?
Home Depot lists decibel ratings, and in this comparison of four Frigidaire models, the largest one (also the most expensive, which suggests they might've included additional soundproofing, or used higher quality components) is half as loud as the others. BTU capacity doesn't seem to correlate with the dB ratings.

When it comes to Haier window units, which specifically optimize for quietness, the 6050 BTU model is rated at 43 dBA, while the 8000 BTU one is rated at 46 dBA.