Some modems take longer than others. Some of the arris modems take exceptionally long, as instead of locking in channels by groups of 8 like some, they do so, a single channel at a time, to ensure the fastest possible connection. That's a hold over from the old Motorola Surfboard line. Slower boot, faster throughput. I have an old DG2460, takes 6-8 minutes to boot, but I can tell you, it's extremely fast, even if it is over 7 years old.
A reboot or restart just turns off and on equipment. A network reset should wipe the current network config and reload it, such as a factory reset would do for hardware. Cox could push an update to your modem so all you'd have to do is reboot.
However, there may be nothing wrong with its config because as others have noted, some modems take a long time to reboot. Is 10 minutes unusual for the OP? I don't know, but it was worth a post.
It's possible that the modem is taking so long to reboot for the same reason you're rebooting it in the first place. If you're rebooting to troubleshoot a connection problem you have poor signal or a modem issue.
Just for a point of reference, my MB8600 takes less than 2 minutes. I do have an excellent signal. I realized a couple of days ago that there wasn't a Cox lock tag on the box, so went out this morning and cleaned out the bugs, snugged up the loose ground wire, and snugged up one of the other fittings. Afterwards, I rebooted and made a point of checking the timing.
Ten minutes is a long time. I'd understand the bloated software of a cable-box taking 10+ minutes...but a modem? I'm not disputing the 10-minutes for other users...but it is a noticeably long time.
There was a recent post about the StraightUp Internet plan and the Add/Change Device link in the Equipment section of our accounts page. I was curious about the Add/Change link and the Reset Device is beneath it. [Yeah, why not] and the reset took only 3-4 minutes. I didn't time it but it was a lot quicker than the song "Coma" by Guns N' Roses (10:14).
Chrispy is correct: OP is rebooting for a reason.
Ha-ha..."bugs." Cox issued my first HD receiver and when I got it home, there was something rattling inside. Further inspection revealed the dried corpses of 2 stinkbugs.