I think this question almost answers itself, but I've learned that's not always the case. It appears from my somewhat brief googling and catalog-trawling that Microchip sells the 3008 and 3208 ADCs. Other than the resolution itself, are there any meaningful differences in these two parts? The price difference is $1 (in quantity) so I realize that if you're building something (or hundreds of them, really) where you only NEED 10-bits it might be worth saving a buck, but for general purpose / hobbyist type applications is there any reason NOT to just go with the 12-bit version? I assume that the interfacing code is all the same across these?
Cost is one factor, as you note. $1 is a big difference in price for a lot of people.
Also consider the complexity in interfacing with the ADC. If it has a parallel interface, you need two extra pins for the 12-bit ADC versus the 10-bit. If it has a serial interface, then you don't need extra pins, but you need extra time to transfer two more bits1. If the serial interface is slower than the ADC, this limits the sample rate, since you can't start reading a new sample until you are done reading the previous.
This is all assuming that everything else is equal. In reality, that's probably not true. A careful reading of the datasheets is necessary to understand all the differences.
1: assuming, as The Photon points out, that the serial protocol used by the ADC doesn't transmit the measurements in octet chunks, in which case either 10 bits or 12 bits requires two octects, or 16 bits.
In addition to Phil's excellent observations, more bits may also mean more iterations of the algorithm underlying the sampling. For example, successive approximation ADC's will need more iterations to yield more bits. This can decrease your effective sampling rate, even for a device with parallel communication. Similar with a delta-sigma, where more bits can mean slower rates. Probably not so with a dual-slope.
Looks like the 10 bit throughput is twice the 12 bit throughput; 200 vs 100 ksps. 12 bit conversion also takes two more clock cycles than 10 bit conversion. What's the more important aspect of your analog signal, precise amplitude, or precise frequency? Would aliasing be a problem for you at maximum throughput?