Yes, 16 is easier. It may be a couple miles longer but not much more than that. I once had a partner who lived in Greybull (east of Cody) who drove both routes regularly during his semi-weekly visits to Gillette. He said the time difference (in his Buick) was less than 5 minutes.
Hwy 14 has a bit more spectacular views going up and coming down, but across the (flat, straight) top it's pretty bland. Hwy 16 doesn't have as many tight curves and isn't quite as steep going up and down, but it has gentle curves and grades the whole way across.
Both are scenic, both are good roads, and both are mountain highways that should be treated with respect. Not too many years ago an older couple descending down the east slope of 16 into Buffalo overheated the brakes on their smallish motorhome and ended the journey inside a store on Buffalo's Main Street. The hubby was killed. Sad. Totally preventable if you mind your brakes (don't "ride" them), but it can happen easily if you ride them too much. Ironically, they probably overheated because he was being TOO careful. It's happened to me once (inching down a jeep trail) when my wife (girl friend then) kept telling me to "slow down," but we were lucky and spared the possible consequences when we reached the bottom just as the brakes totally gave out. I'd been down that trail dozens of times. Brakes were hardly needed at all, but this time I had a gal with me who was frightened of mountain driving. Brake fade was the last thing on my mind.
Just to be clear, when your engine braking isn't enough to slow you for the next curve, brake fairly hard until you've slowed below your target speed, then leave your brakes alone until your speed builds up to or beyond the target speed and brake hard again. DO NOT use light brake pressure to maintain the speed. That'll kill ya on any mountain. There are pull-offs where drivers are encouraged to stop and check the brakes for heat build-up. Use them if there's any doubt at all.