Albuquerque is always our first and last night going to and from Arizona. We've traveled all three routes mentioned in the last several years in the MH and toad.
We don't like the Flagstaff route due to the traffic on I40 and I17. The normal north to south or west to east winds can be a real bear on I40. Also lots of truck traffic and aggressive drivers between Flagstaff and Phoenix metro. Just be sure to do it during non rush hours.
The route from Globe to Holbrook is our preferred route. Yes, it is a slow, long and twisty descent and pull out of the Salt River Canyon and you can get snow around Payson and Sho Low, but it is a good road. We just watch the weather and run between storms. You could get a spring storm in early April, but it would melt quickly.
This year we went south on I25 to Hatch and Deming. I25 was an easy route and had surprisingly light traffic. We took this route in December to stay at Tombstone Territories for 10 days. The traffic around Tucson and up to the Phoenix area is pretty heavy. Don't see how it could be a safer route, and it would be significantly longer than Globe.