Life sucked for everyone until very very recently. And still does for many people. I don’t know what’s worse though, having to go to war or having to have ten kids without modern medicine.
You don’t always go to war in a far distant land, sometimes the war comes to you.
Sucks to be raped and pillaged by the invading forces.
Like, oh my God. Plague sufferers - sooo gross I can’t even #outdoorssux
clarification: they weren’t plague victims. They were her victims
(also scary is that I always had a thing for the Italian Catholic princesses in the other neighborhood)
Curses, my lame attempt at humour brought down by historical detail! 
To answer the question: modern-day princess. I need my mod-cons.
I’m pretty convinced that happiness only very slowly increases with more modern comforts (assuming one has never experienced them). If you don’t know what air conditioning is, you don’t miss it that much. Summer is hot; that’s the way it is.
But the suburban princess --on average – has a lot more control over her relationships, so I’d probably pick that. If I could guarantee a good husband (even if that just meant one who was fine with a marriage open on both sides), I’d consider harder.
There was a girl on an episode of wife swap (or trading spouses…one of those shows) who was whining and bitching to her dad because the hotel suite only had two bathrooms.
I’d take that life in a second over anything the princesses of yore had.
I believe the Great Plague was in the 1400s. Smallpox would’ve been the big worry.
There were any number of localized plagues that were equally deadly. The Great Plague of Seville in 1647 is thought to have killed half a million people and that would certainly have worried me if I’d been there.
There’s no mention that reincarnation is limited to same gender, so I’m going to play.
I would pick the modern day princess any time. The only three things I could think of the old day princess has and the modern day princess doesn’t have are : fancier clothes (and even that is arguable), more spacious living quarters, and more leisure time (probably, but to do what?). The modern days princess avantages are innumerable, on the other hand.
To say the truth, I wouldn’t even take a modern day actual princess (hunted down by papparazi, compelled to attend boring events all the time, certain that every single thing she does or word she pronounces might be misreported on the front page of papers the next day…) over a modern days “princess”, so…
If the other option was at least being queen (can sent whoever you don’t like to the gallows and whoever you like to your bed, while being forever remembered in history books for your great reign and the improvements you brought to the kingdom, despite the large number of people you had hanged or bedded), I could have considered the option for more than a microsecond, but a princess, really…
Except when it was the queens being sent to the gallows – especially since you really weren’t able to bed who you wanted. Depending on who your husband was, you could lose your head. Not to mention if you pissed off your subjects, you might as well kiss your ass goodbye.
Marie Antoinette, Mary, Queen of Scots, Anne Bolyn, etc. Not exactly remembered for dying peacefully in their sleep. 
Modern …for the money.
You kinda stacked the deck for the modern “princess.” If you’d allowed for a true princess in modern times, it becomes more interesting. Especially since you defined modern “princess” to just be a suburban daughter, rather than the rich girl whose daddy buys her everything that I would have assumed.
I’d rather be a modern suburban “princess” than an ancient princess. I’d rather be a modern princess than a suburban “princess.” And I’d rather be a rich “princess” than a modern princess, due to the lack of responsibility.