We didn't change hotels much. We had a full week at the same hotel in Scotland and then the same in England. It was why I booked a bunch of one day tours where we could have a home base instead of moving around a lot. Just know for the Mediterranean the ports are about an hour or two from the city so there will be a lot of bus traveling.
That is true for some Mediterranean ports, but not all or even most, depending on the cruise. I have done some of Europe by land. It is fantastic and I highly recommend it. My favorite part was staying a family-run B&B's and getting a chance to really talk with the locals in the morning over breakfast.
But, as others have said, there are advantages and disadvantages to both. Yes, you can make your home base one hotel in Europe, but that will also restrict what you can reasonably see too. Otherwise, you are switching hotels every day or two, packing and unpacking. You are also spending significant time traveling. Those two things are time that you aren't seeing sites or relaxing (though the travel between places can be great in itself).
We are scheduled for the Disney Greek cruise in 2020. We will be spending four days in Rome prior to the cruise, then we get to see Sicily (which we would probably never make it to outside of a cruise), Athens, several Greek islands (which would take significant travel time to get to on their own), and the Amalfi coast (which is super high on our bucket list). To see all of those places in 9 days, without the huge time suck it would take to travel between each place, the planning and stress of transfering, packing and unpacking daily, and the risk of travel delays, etc. is a huge plus for us. Yes, we only get a flavor of each place, but that actually suits us well. Although we are in our early 40's, and in pretty good shape, we are still pretty low-energy people when traveling. If we really love a place, then we can revisit on a land trip.
We have also had some serious bad luck with accommodations that look great online, with great reviews, but were pretty nasty in person. To see all these cool places and return to the same room, clothes unpacked, guaranteed to be clean and comfortable, will be really nice for us. I travel with three ladies (wife and two teenage daughters), so just the cosmetic/toiletry unpacking and packing situation alone is great to avoid.
We also get a chance to eat locally for lunches (and even dinner if we want in some places), we are guaranteed one to two meals that we know will be good each day, and it is served by a wait staff that we know and who knows our likes and dislikes. Plus, not haggling with the teenagers about who wants to eat where. I love local food and trying new things, but it is often hit or miss in Europe and finding a place to eat can be a challenge on its own (including finding a place open early enough for dinner to fit our normal routine). We get the best of both worlds this way.
The entertainment as we relax in the evenings will be fun.
Add to that the two sea days for forced rest and relaxation, and cruising the Greek isles this way is a dream come true for us. I don't doubt a land trip in the area would be great too, but we wouldn't see nearly as much in the same period and doing it with two teenagers wouldn't be ideal.
