For my Thanksgiving travels, I realized I left my basal thermometer at home. No big deal; I swung by a CVS pharmacy and picked one up. I actually really liked the new CVS one--it didn't beep throughout, and it had a flexi tip that was more comfortable than my first.
I'm not sure why I did this, but when I returned, I took my temp with the new one, and then with the old one. Old thermometer during the day registered the expected 98.6. New thermometer was at 97.5! I did this a few more times and found that the new thermometer was consistently much lower than my old one.
I suppose if I always used the new one, my temps might still show a pattern change. But lesson learned: stick with the brand you have!