A true SPL Meter is certainly better than a Phone App, at least, based in the information I've been able to gather.
Though some may be better than others. I know there are very high quality mics available for iPhone (etc...), but they are not cheap. In a sense, you get what you pay for. The built-in mic of a Phone is intended for voice use. That is actually a pretty narrow range. These mics are not calibrated for high fidelity. They might be OK for broad and general sound measurements, but I wouldn't trust them with a frequency response plot. Again, there are high quality external microphones available, but do not expect them to be cheap.
Most meters have two weightings - A and C.
"A" weighting covers 500hz to 10,000hz. This is used for very broad and general measurements. For example, if you want to check noise level in a industrial situation, you are more concerned with the SPL and less concerned with the frequency response.
"C" weigthing covers 30hz to 10,000hz. This would be used when there more precise frequency requirements. For example, when you are testing the frequency response of a speaker. I've done this to all my speakers, plotted the bass frequency response. Though in my case, I'm not really concerned with anything below 30hz, so I don't need compensation files.
As to the response of a meter changing over time. Likely it is like a speaker being broke in. Over time the surrounds on the microphone diaphragm soften from use. But, given the small size, I don't expect it to be much.
There are places that will calibrate your meter for you. Buy the meter, use if for about a year. Then send it in, and they will compare it to a know industrial/Studio standard system, and send you back a calibration file. That way you have the precise calibrations for your specific meter.
Although, as I said, there are countless generic Radio Shack calibration files out there. These should be sufficient compensation for hobby use.
Search Google for 'Radio Shack Sound Level Meter Calibration Files' and you should find several of them. Take a look at the deviation, and I think you will find that within any realistic working range, the deviation is pretty small.
Steve/bluewizard