We are recording interviews inside a studio setup. Mostly 2 people or a maximum of 6 people will participate. The noise floor is around 55-60dB, and we want to reduce it to at least 80-85dB. Shall we buy a digital mixer or upgrade to a better analog mixer? (The current one is a Behringer 16 channel model).
Good analog mixers can be pretty quiet. At one point of time, however, you are likely going digital and a digital mixer already does that which helps. But the noise floor of your interview setup is very likely determined mostly by your microphones. Behringer is not exactly renowned for quiet preamps but with a reasonably "hot" microphone signal (like produced by reasonably good(!) large diaphragm condensors, and no, "professional studio quality" microphones for $20 are neither good, professional, or studio quality) the impact on the noise floor should be tolerable.
You don't state just how you go to digital and/or recording: that may also impact your noise floor of course though equipment starting from a balanced line-level signal (like a mixer should output) needs to be pretty bad before it has significant noise floor impact. Like a laptop input.
I use smaller Behringer mixers than 16 channel regularly, and have used bigger ones, and there is no discernible noise from them. If you only have 6 mics max., why do you have 16 channels..?
Every component in the chain could produce noise. Cheap mics, being the first in the chain, can easily be a cause. Next, and easy to sort, are cables. Even an expensive mic will struggle to deliver through a cheap and nasty cable - it's probably the most likely cause of noise, and most overlooked link.
Setting up the eq, trim and other controls properly will also clean things up.
While this doesn't answer the question directly, there are important factors to check. With them sorted, you may not even have to consider answers to the question!
If the recording signal chain is analog, for example: mic > preamp > mixer > recording media, i'd check the S/N ratio for each component in order to rule out any bottlenecks in signal quality besides the mixers specs.
I might be out on a limb here, but there's a chance that the question of digital vs. analog mixer isn't as important as the quality of the DA/AD converters in the preamps.
In other words, a new mixer could improve recording sound quality as long as everything else is up to par. You might find that the weakest link is someplace else.