Among the other things listed above are some of the intangibles.
For me (and your mileage may vary), there is less set up time as the HW has a number of things built into it that I used to have to carry along and set up. This also translates into less stuff in the isle when popped down or during travel. I used to have to stuff all of the seat back cushions into one end and work really hard to not cover up access to the refrigerator with the rest of the bins, chairs, EZup, etc. Now, I have enough room because all of that stuff is actually stored somewhere or no longer needed, I have room and the actual height inside to put the kids bikes inside when it is popped down.
We went from a standard 10' box to a 14' high wall box and the difference is how things work and flow inside is dramatic. For times when we are stuck inside, we are not crawling all over each other. We don't have to do the infernal "stuff shuffle" of moving a suitcase, bag or tote from one spot to the next to the next while trying to sit or access the limited storage areas.
Having an oven is a nice thing on the few occasions we've used it. Having gone so long without one, it is hard to remember we have one and plan meals accordingly. Anyway, the built-in microwave was also a great inclusion as we brought along a small one that sat on one of the two countertops in the previous PUP. My wife refuses to go microwave-free camping although we barely use it. I have decided other battles are more worthy.
The hard wall bathroom is not just hard walled but it is bigger, about 50% more space. There is a full size porcelain toilet in mine plus a decent sized shower pan floor. There is a curtain inside to use when showering but because of the added room, it doesn't feel like the curtain is clinging to you every time you slightly move. We don't use the shower so much but it's another "nice to have" on those rare times.
I will also give you some of the disadvantages as I see them.
Having to wait in line to dump my black water tank with all of the other big rigs who have quite the ritual and process to dump their systems. This is purely a function of my unit having a black holding tank instead of a cassette potty. I would strongly recommend a cassette potty. It would be SO much easier on pull out day to walk the cassette over to the toilet and dump it than waiting in line, plus a little added care.
The HW is definitely heavier and taller. Even before I did the over/under axle conversion, it blocked my rear view mirror, which is definitely an advantage of a typical PUP. I had to get mirror extensions because, for all intents and purposes except for gas mileage, I have an equivalent small TT when towing and backing. Thankfully, the front profile is still about the same as the TV but just barely. I dropped almost a mile per gallon when going from a standard PUP of about 1,600 pounds to a high wall of about 3,400 pounds. Not bad at all, but I know the difference during acceleration and climbing on grades. Stopping is actually better as the HW has brakes whereas the standard did not. Once I dialed in the brakes, I cannot tell the HW is back there during normal stopping. I can only imagine the assist those brakes will give during an emergency situation.
While nothing would prevent me from going back to a standard height PUP, I sure wouldn't just want to do so. We get many of the benefits of a PUP and a TT, and some of the drawbacks of both.
It all comes down to what you want out of your rig.