The honest version
People compare these two because of one number: the nightly rate. Jersey City is usually cheaper than Lower Manhattan, sometimes by a lot, and it's close enough that the trip looks free on a map. Then you actually take it four times a day.
Here's how we'd think about it. The PATH ride itself is short. Exchange Place to the World Trade Center is a few minutes under the river, and Grove Street adds a stop. What costs you time isn't the ride, it's the whole sequence: walk to the station, wait for the train, ride it, walk out through the WTC hall, then walk to where you were going. Realistically that's 25 to 35 minutes door to door each way, every time, and it's the same in reverse when you're tired at 11pm.
On a four-night trip with two people, that's roughly four hours of your holiday spent under the Hudson. Whether that's worth the savings depends entirely on how you travel. If you're out from 9am to 11pm and only sleeping at the hotel, Jersey City makes real sense. If you have kids who nap, a work schedule with gaps, or any intention of going back to the room to change before dinner, staying in Manhattan pays for itself in a way the booking page doesn't show you.
The other thing worth knowing: PATH schedules change late at night and on weekends, and which line runs where isn't the same at 2am as it is at 9am. Check the PATH app before you plan a late night out, because the fallback is a cab through a tunnel with tolls.
Where we sit in this
We're on John Street in the Financial District, so we're not neutral, and we'd rather say that plainly than pretend otherwise. What we'll defend is the specific claim: from here you walk to almost everything people come downtown for, and you're on the Manhattan side of the river when the night ends. Our suites have kitchens and a laundry room in the building, which is the other half of the budget argument. If the reason you were looking at Jersey City was cost, cooking a few breakfasts and doing your own laundry closes a real chunk of that gap without adding a train ride to your day.