Depends on how you define "see". You're in AUH for about 45 minutes. The flight between Muscat and Abu Dhabi is only about an hour, going late night and returning very early morning. They didn't serve food on that short sector, either coming or going, but I am sure that if you asked then you would get something. It's only about an hour-long flight.

Both Muscat city and Muscat airport are safe. As for turnarounds, Dubai is just a lot more modern. Irrelevant example, but one nonetheless, it has never taken me more than 10 mins to go through immigration and that is with a line. In Muscat, everything was by hand and it took about an hour or more to go through the visa on arrival and there were only five of us. Fortunately, I got some rial in Al Ain when I was there which sped things up a little since there was one less line to stand in. There is little shopping but the lounge is nice. It's the Oman air lounge and pretty decent. But, again, nothing compared to DXB. As far as the cities, they are just different. Muscat is probably arguably more interesting, exotic, and arabic, but they are just different and each appealing in their own rights.