The short version
Stay on the Upper East Side if you want to sleep, walk to Central Park and the museums, and have dinner somewhere you can get into without booking three weeks out. Stay in SoHo if shopping and downtown restaurants are the actual reason for the trip and you want them under your window.
That's the whole decision, and it usually comes down to one question: do you want your neighborhood to be the attraction, or the place you come back to when you're done with attractions? SoHo is the first. We're the second, and we're not neutral about it, so read this knowing we live on East 62nd Street and chose it on purpose.
What each one is actually like
SoHo runs roughly from Houston Street down to Canal, between Sixth Avenue and Lafayette. It's the cast-iron historic district: Greene and Mercer Streets are still Belgian block, the buildings are 19th-century warehouses with fire escapes down the front, and the ground floors are almost entirely retail now. Broadway between Houston and Spring on a Saturday afternoon is one of the densest pedestrian stretches in the city. Restaurants like Balthazar on Spring Street have been booked solid for thirty years. It photographs beautifully and it is loud until late, because the streets are narrow, the bars are on them, and delivery trucks start on the Belgian block around 6am. Green space is thin: Washington Square is a walk north into the Village, and there's no park you'd call yours.
The Upper East Side starts at 59th Street and runs north to 96th, from Fifth Avenue to the East River. The avenues work (Lexington and Third have the food, Madison has the shopping, First and Second have the neighborhood restaurants) and the numbered side streets between them are residential, low-rise in stretches, and quiet by 10pm. Central Park is on the western edge, and Museum Mile runs up Fifth from the Met at 82nd. Down at our end, in Lenox Hill, you're eight minutes' walk from the park entrance at Fifth and 60th, a block from Bloomingdale's at 59th and Lex, and two blocks from the F and Q at Lexington Av/63rd St.
They're 20 minutes apart, which matters more than people think
The 6 train from 68th St-Hunter College to Spring Street takes about 20 to 25 minutes, no transfer. From Lexington Av/63rd St the Q to Canal Street is comparable. So this isn't a choice between two cities. You can stay uptown and eat dinner in SoHo four nights running, and the ride home at 11pm is a seat on a mostly empty train instead of a fight for a taxi.
The reverse is less true in practice. If you stay in SoHo and your days are the Met, the Guggenheim, the zoo, and the park, you'll spend an hour on trains every day getting to them and back.
Price and space
SoHo runs expensive per night and small per square foot: it's a district of converted commercial buildings, so hotel rooms tend to be tight and apartment stays tend to be one-bedrooms. The Upper East Side is where the families live, which means the housing stock is bigger. If you're four people or more, this is usually the deciding factor, not the vibe. Two rooms downtown often costs more than one apartment with two bedrooms up here.
Who should pick which
Pick SoHo if: you're two adults on a short trip, shopping is a real agenda item, you want to walk home from dinner in eight minutes, and street noise doesn't wake you.
Pick the Upper East Side if: you're travelling with kids or parents, you want Central Park in the morning without a subway ride, you're staying a week or more, you're in town for something at Memorial Sloan Kettering or Weill Cornell, or you simply sleep badly in loud places.
We're on East 62nd Street, between Second and First. Apartments rather than rooms, sizes from a studio up to the whole house, and your own front door instead of a lobby. Midtown's best blocks are the quiet ones, and that's the part SoHo can't sell you.