So we're talking about the Elizabethan era. I'm assuming you want us to ignore the customs and politics and religion of the era (which made life a little complicated for monarchs).
I don't think the availability of sexual partners is a factor here. A great looking, confident, charismatic recent grad can readily sleep lots of women with little to no effort. A sheepish, ugly king would face lots of rejection. He really didn't have the power to make them have sex with him. Plus, he really wasn't supposed to be having sex outside of marriage. Women today are much more attractive than they were then too.
I think the recent grad wins, by a long shot. All the little modern conveniences are too much to compete with. A palace would still be either really cold all the time, or unbearably hot. A recent grad has air conditioning and heating. Being able to sh.it in private, and being able get rid of the excrement easily is great. Kings weren't able to take 20 minute hot showers everyday either.
Food in England is terrible to this day, can you imagine how awful it was in the 1500s? The East India Company basically took over the world by selling pepper. A recent grad can get any type of food from any part of the world, and probably have it delivered to his door, cooked and hot, with less than an hour notice. I had Korean BBQ delivered the other day. It was incredible.
The entertainment options are also great relative to the 16th century. Shakespeare and the theater were big deals because people then had basically no way to entertain themselves before that was available. People must have been so bored all the time, especially kings who didn't work.
High infant mortality also sucks. I can't imagine having a child and watching him or her die. That would be the most horrifyingly sad experience I could go through. Having a bunch of kids die would be so much worse.
Kings would still be exposed to terrible diseases like small pox and cholera. Have you ever had either of those? You probably don't want them.
Traveling anywhere would be miserable. As soon as you leave the palace, the streets would just be filled with sh.it. Getting anywhere would take weeks or months. And you would spend the entire time in a tiny box just staring at the wall (if it was cold). A recent grad can probably afford to fly to the other side of the planet. It will take less than a day, and he'll spend the whole time watching recently released movies.