Ideally, a converter won't have any "sound". It will just transparently pass through the signal. From the spec sheet you can check things like
- dynamic range/signal to noise ratio
- the amount of hiss that the converter will add to your recordings. 24-bit converters aren't inherently better than 16-bit. They need to actually have lower noise or the extra bits provide no information. The dynamic range spec tells you more than the bit depth.
- equivalent input noise
- the amount of hiss the mic pre will add
- total harmonic distortion
- distortion creates extra frequencies that weren't present in the original
- frequency response
Unfortunately, you can't always trust specs to be accurate. I've seen products with worse specs than the actual product delivers, and vice versa. Some companies are better about this than others.
Also, things like power supply noise can vary from one situation to another and won't show up in the specs.