The NEC shows that #3 Al has a amp rating of 85 amps @ 90 degree Celsius or 194 degree F. If this was me, and I was wiring from the 100 amp breaker on the genset back to the ATS I would jump up to #2, it's rated at 100 amps. #3 copper THHN has a amp rating of 110 @ 90 degree C. I typically use copper wires in conduit for my installs.
As for the #14's that would work just fine, it's what I use.
Check your local codes or with your electrician to make sure your installing something he'll approve of. I'm sure he'll answer any code questions.
Depending on which code cycle he is on nether one of those sizes will work. First you do not size the wire by the 90deg. column unless you have some super heat resistant equipment. For a standard gen. and ATS the terminations on the equipment will be 75deg. That is the column you use. If he is under the 2005 code then it would be #1alu or #3Cu. But if he is under the 2008 or 2011 SER cable has been derated into the 60deg. column which would change it to 1/0Al or #3Cu THWN in conduit
I have purchased a Generac 5875 with 200 amp SE rated ATS. To save on some of the installation costs, I intend to do some preliminary wiring from generator back to the transfer switch, then having electrician make utility and meter connections to ATS. The main breaker from generator is 100 amp 240v, and the unit is rated at 83 amps at 240v. My local electric supply house suggested a 3-3-3-5 SER aluminum armored cable for the generator to ATS power feed. For the dc and control wires, we are looking at single 6 conductor 14 awg THHN in aluminum armored cable. The run from generator to ATS is about 30-35 feet. Do those cables make sense? Any input would be appreciated.
I hope you do not plan on direct burying this cable. The aluminum will last about a year in the ground.