I am going to take a little different perspective on this. I have two children, ages 11 and 14. They have been on about 25 cruises. We started cruising Europe with them about 7 years ago (ages 4 and 7) and it has paid dividends like you would not believe.
The first cruise was on the Celebrity Millennium out of Venice. We visited quite a number of ports including Rome and each port was seen as a new adventure. Yes, Rome was a longer day, but having been in the Coliseum had a great impact in the years following...as did their first gelato. In Florence - which you think would be the most boring of places - we had a fantastic private guide that knew how to engage the kids. (One of my favorite photos is of my daughter sitting on my shoulders with the "other" David in the background.) Remember children see things differently, so you will be amazed at what they pick up on...especially when viewing things from a lower height!
Fast forward to last year (and after many cruises) when we visited Israel and Egypt on the Celebrity Equinox. I would not shy away from Egypt once you are there...but it is getting there (long drives) that can undercut any value with young children. (I have lots to say about the dirt and constant badgering for tips, but that is another thread.) My kids loved it (we overnighted in Cairo) but we all agreed that one time was enough.
This year: My son is going on a 19 day Student Ambassador trip with other kids his age and will be visiting Venice, Rome and some other places he visited when he was younger. He is excited to see them again...on his own terms. Just something to think about. I am sure you kids will down the road.
As far as quality children's programs, Celebrity's is excellent. There will be plenty of kids, but not too many. And as far as cruise products go, Holland America and Celebrity are both premium lines. I find the ships, service and food to be better on Celebrity (especially its newer ships), so I would think hard not only about the quality of your children's cruise, but yours as well.