I personally have worn CIC (Completely in the canal) and ITC (In the canal) - full canal and MC (Micro canal) or full shell/half shell.
The sound quality has always been good. No better or no worse than BTE or RIC (Receiver in canal) styles.
In terms of the functions, as you put it, this is where the differences may lie.
A custom in the ear aid is less likely to have 2 microphones. Some do - for example, the Phonak Virto in the ITC MC, or ITC, or full shell ITE form factors. But the CIC or IIC form factors do not. I believe the reason being that the aids are too small to place the microphones side by side. The disadvantage with not having 2 microphones is that there is a loss of beamforming capability which means you have less directionality and as a result you would have more difficulty hearing in noise. However if one wears a CIC or IIC then one has their pinna exposed and this I believe acts as a natural filter to eliminate background noise, so the loss of directionality is compensated to a certain extent.
The other main difference in functionality is to a degree bluetooth. This is always available on aids with a BTE/RIC style but is not always available on custom styles, particularly IIC or CIC. But I believe it is becoming more widespread.
The more severe ones loss, the more suited to BTE/RIC. Although quite severe losses can be fitted in custom.
The BTE/RIC styles are better in terms of fitting deteriorating losses. If someone loses a substantial amount of hearing, a BTE can be reprogrammed or a RIC can have a more powerful receiver fitted. This differs from a custom in that the custom would have to be replaced outright, say, when going from a CIC to an ITC.