I've not worked on these type of coolers, so bear with me... I have used demister pads and water sprays to increase the capacity of large chemical plant multistage centrifugal air compressors in East Texas so I think I understand the principle even if the equipment differs greatly. Granted, Phoenix is much drier than East Texas.
Sounds like you've already checked the things that make the most sense. So let's assume that the pad/duct/water supply systems are behaving the same. What about the air flow? Can you stick an anemometer in the duct work at the same point on both systems to measure feet/sec or some such? (I've done this with my home HVAC before using a cheap hand held anemometer to see what the blower was really doing.) Does the one with the lower temp (higher delta T) show a substantially lower flow? If so then the problem might be one of air flow rather than total duty. Perhaps the one with the low delta T is actually pulling through substantially more air? Q (duty) might be similar but the overall flow is much different and therefore so is temp. This seems unlikely, but without seeing the blowers and ductwork of the two units I can't rule it out. I've seen subtle differences in gear in "identical" plants result in notably different operation that perplexed sharper engineers before me on the same unit (one of them became CEO of our $5 billion dollar/yr operation), before I figured out what differed that had been missed before.
Have you considered swapping the pad sets between the two units to see if relative performance changes? (I suggest this because I suspect it is easy to do and will give good info about where to look.) This seems like a longshot, but perhaps the configuration or orientation of the pads differs in some subtle way. If it doesn't make any difference in performance after the swap then you can rule out the pads/configuration.
Measuring water supply temp and water flow is straightforward. Have you done this? Yes it is probably a waste of time, but bucket flow measurements can turn up all sorts of surprises (been there, done that...sometimes a flowmeter orifice or other device is FUBAR or doesn't match its calibration.)
Something differs a lot if the temp delta you reported is representative. The question is "what differs?"
