Need advice re: yellowstone driving routes
 

Fine tuning an upcoming trip end of August to Yellowstone. We will be flying into Bozeman, arriving around 1 pm, staying 3 nights at Canyon Lodge, one night at OFI then down to GTNP for a few days then flying out of Jackson Hole. ON our way to Canyon Lodge, plan to stop and see Mammoth area attractions. Would we be better off taking the loop from Mammoth down through Norris and over to Canyon, or east to Tower area, then down to Canyon? I understand there is road construction between Mammoth and Norris, which would make me think the other route would be better. The mileage is pretty even between the two. Difficult to judge without being there and knowing what the drives are like. Time will be an issue, especially if our flights runs late. Any advice would be appreciated. Has anyone been there recently?