On several occasions I have moved very high antenna / very low power stations to a location that was lower with higher ERP and found ratings to increase significantly.Yup, big power drop. They may get a better location, but they're going to lose a lot of whatever punch that signal has currently. And that isn't exactly a whole bunch of punch, even now.
A more recent example was moving 98.3 in West Covina (LA Metro) from a higher location but with less than 1,000 watts ERP. We moved it to pretty close to 6 kw at 100 meters, and ratings tripled, pushing the KRCD KRCV simulcast into the top 10 in LA in its target demo.