There are three issues here:
1)
The rating of the compressor. Consumer oriented compressors are notorious for claiming a horsepower higher than theoretically possible. I have small Craftsman 110V that runs on a 15 Amp circuit just fine and claims to be 7.5 "peak" horsepower. I also have an industrial Speedaire 2-stage compressor that needs a 50 Amp 6 gage circuit. The speedair is also listed at 7.5 hp.
2)
Rating of wire size: If your compressor needs 16 Amps then you should have 12 gage wire. By the book (and there are some exceptions for motor inrush, run length, conduit, etc) here are the guidelines:
14 Gage: 15 Amp
12 Gage: 20 Amp
10 Gage: 30 Amp
8 Gage: 40 Amp (for larger sizes, the exceptions start to matter)
6 Gage: 50 Amp (for larger sizes, the exceptions start to matter)
It does not matter if the circuit is 220V or 110V for the amperage rating (if questions about why this is true, post back and I'll do my best to explain).
In the NEC, there is significant exception in wire size for running electric motors. The reason is when an electric motor starts, it uses a huge amount of current compared to it's "normal" operating current requirement. The NEC recognizes this and allows you to use a wire size based more on normal than start current. If you had to size for start current, that would be much larger wire. You are also allowed to use slow blow fuses for electric motors.
For you application, since you say you need 16 Amps, you will need 12 gage wire as a minimum. 10 Gage is great if you have it but not strictly required.
3)
Romex (NM or NM-B) in conduit: There is debate wether or not NM wire can be used in conduit and still be code compliant. I've looked hard for this in the NEC and haven't found a clause prohibiting it for inside use (can someone prove me wrong on this, please?). However, most inspectors where I live will fail you for running NM in conduit. It's clear by code that NM is not allowed in conduit for underground or outside applications.