KeithRB:
Assuming that you are not in the noise, which you shouldn't be if you choose the divider correctly, 4196 steps at 5 V gives you the same resolution as 4196 steps at 15 volts, you are not losing anything.
I was refering to usable information, so noise is a potential factor unless everything is in a Faraday cage. No matter how well chosen the divider configuration is it can't prevent EMF induced noise as it travels from the output of the divider to either an analog pin on the Arduino board or a separate ADC chip. Divide 4196 steps into 5 V and then into 15 V, that will give you what the respective difference if voltage is between each step for each voltage level. 15 V is simply going to be more tolerant, as in a given level of noise is going to impact the ultimate digital signal level less than at 5 V.
Obviously, a voltage divider right next to an Arduino's/ADC's input pin will be better in either cases than one that has to go an inch or more through a wire or trace. If there are chips with voltage dividers on the same piece of silicon as the ADC that would be the closest to ideal as possible. That's why I suggesting looking to see if such a thing was available (if I knew such a thing existed I would have linked to an example). Depending upon the application it might not be necessary, but IMHO it's worth a little time to investigate the possibility.
Docedison:
voltage divider going from 5 to 15 V down to 0 to 5 V means there will be roughly three times less 1/3 less usable information detectable in the output signal
so change the Vref as required to increase the effective available information by providing a Vref suitable to the measurements.
Thanks for the correction, I was conflating a couple of different ideas in my head while typing... 
As for the VRef, in a Arduino it can be anything on a range of 0 to 5 VDC and the default for most Arduinos will be 5 VDC. Unless you are refering to doing the ADC outside of the Arduino with the signal at a higher voltage level, I'm not sure what changing VRef on the Arduino would improve.
retrolefty:
I suspect you will have a very hard time trying to find, if any indeed exist, any ADC chips that allow input signal voltages to be higher then it's Vcc voltage (or lower then Vdd), which in most cases I'm aware of is limited to standard Vcc values of 5 vdc or lower. And any ADC type module that can handle that high of input voltages would just be using some kind of programmable front end attenuator (voltage divider) and still process the ADC conversion at standard Vcc values.
As mentioned before I didn't know of any off-hand. If they do exist they would be potentially better, even if they used chip-level voltage dividers to step-down to 5 V or some other VCC level, than implementing a voltage divider by either through-hole or surface-mount resistors for reasons I also mentioned above. An exhaustive search is probably not warrented, but in my mind perhaps 15 to 30 minutes of Googling would be justifible.
Edit: Looks like CrossRoads found something similar while I was typing.