The short version
Pick the Financial District if you want space, quiet nights and the harbor. Pick Greenwich Village if you want the bar, the restaurant and the jazz club to be the reason you're downtown in the first place.
We're at 17 John Street, so we'll say up front where we stand. We live in FiDi and we like it. But we send guests up to the Village all the time, and there are trips where it's the better base. Here's the honest split.
What you're actually next to
In the Financial District you're next to the water and the big downtown landmarks. Wall Street is two blocks from our front door. Stone Street, the cobbled restaurant block, is a short walk south. The ferry terminal is about five minutes on foot, which is how you get to Staten Island, Governors Island and the Statue of Liberty boats. One World Trade Center, the 9/11 Memorial, South Street Seaport, Battery Park and the Brooklyn Bridge walkway are all inside a twenty-minute walk of each other, and you're standing in the middle of them.
Greenwich Village puts you next to a different set of things: Washington Square Park, the brownstone side streets west of Sixth Avenue, the restaurant blocks around Bleecker and MacDougal, and the small music rooms that have been there for decades. It's low-rise, leafy and mostly residential once you get off the main streets. What it isn't is close to the harbor. If the ferries and the bridge are on your list, you'll be riding down to them rather than walking out to them.
Evenings feel completely different
The Village is busy at night, every night. That's the point of it. You walk out at 9pm and there are twenty places within three blocks with a wait. If you're travelling with friends, or you're the kind of person who decides where to eat by walking until something looks good, that's a real advantage.
The Financial District has good nights, but they're concentrated. Stone Street fills up after work and stays loud into the evening. The Seaport has bars and a rooftop or two facing the water. Beyond those pockets, streets clear out. Some guests read that as dead. Most of ours read it as being able to sleep with the window open and walk home without weaving through a crowd.
Weekends are FiDi's best trick
Saturday and Sunday down here are quiet, and it's genuinely lovely. The office crowd is gone, the sidewalks belong to whoever's out walking, and you can stand on Wall Street with almost nobody around. Coffee and breakfast are easy to find, restaurants are open, and you're a short walk from the water when you want something to look at.
The Village doesn't have an off switch in the same way. Weekends there are the busiest part of the week. Which is fine if that's what you came for, and tiring if it isn't.
Space for your money
This is the part people don't think about until they've unpacked. Village buildings are mostly old and small. Charming, but you're often in a compact room up a narrow staircase.
Downtown has newer, taller buildings, and that's where you find apartment-style suites with real kitchens and multiple bedrooms. Ours run from studios up to two and three bedroom apartments, and the three bedrooms come with either two kings and a queen or two queens and a king. When you're four or five people, or you're staying more than a few nights and you want to cook and do laundry, that difference matters more than being four blocks closer to a bar.
Getting to the rest of the city
Both are well connected and both are walkable. FiDi's advantage is that it sits at the bottom of the island where a lot of lines converge, plus the ferries. The Village's advantage is that it's already halfway to Midtown, so if your days are spent uptown you'll shave a few minutes off each trip.
Either way you should plan on walking more than you expect. Downtown blocks are short and crooked, and the distances between the things you want to see are smaller than they look on a map.
So which one
If your trip is landmarks, harbor, the Brooklyn Bridge, kids, a work stint near Wall Street, or anything longer than four or five nights, stay in the Financial District. If your trip is dinner, drinks, music and browsing, and you'd rather be in the middle of that at midnight than a subway ride from it, stay in the Village. Both are the right answer for somebody. Just don't book the Village and then complain the street is loud at 1am, and don't book FiDi expecting a block party on a Sunday night.