There really isn't a "best."  They won't eat or drink after dark, but the will want food and water first thing in the morning. 
 
If feed is outside, it will ruin if it gets wet, and can get them sick if they eat it and it is molded.  But, mice won't be attracted into your coop.
 
If water is outside, and your chickens are locked in the coop, the chickens might want to drink before you let them out -- which can be stressful or even dangerous in hot weather.
 
I keep both inside because I have a large, airy coop that they are usually in during the heat of the day, for the shade.  I rarely see a mouse in the coop.  I do keep some bromadiolone rat poison in a chicken proof container in there, but I only saw a few mice over a couple of years before I started doing that.
 
If you have a very small coop, a feeder and waterer can really cut down on their available floor space -- but then, a really small coop in the south is likely going to be too hot for them.
 
Actually, in the south, a good type of coop is three sided and continuous with the run, if they are not free range -- so they can some and go as they please.