Beijing or Shanghai on day layover?
 

If you had a choice between a 10 hr. layover in either Shanghai or Beijing, which one would you opt for?

where did you move it to?

Depends upon your interests. And how you handle smog. If it's museums then both offer enough to take up a few hours. From PVG you can hop on the subway line 2 (green) for 7Rmb and be at People's Square in an hour (quick transfer across the platform mid-trip). From there you can get just about anywhere in the city, or just walk over to the Shanghai Museum and City Planning Pavilion, then meander along Nanjing Road, rather west or east toward The Bund. The new China Art Museum (old China pavilion at Expo) is five stops away on line 8 (blue).

From PEK you can also hop the rail service which connects to the subway system, then do the circle and cross city lines to Tieneman (sic) Square. Lots to see here, from the Forbidden City to the new National History Museum, then walk over to Wangfujing Street and check out the big department stores before heading back to the airport.

The subway systems in both cities are easy to navigate, with English signs and most announcements, albeit crowded (so check your bags at the airport). You'll need at least 50Rmb in cash for tickets. Most museums are free and you can use a credit card for any meal you might eat downtown (unless you're doing small street food outlets).

I've done both cities this way on a day transit.

I assume that if I only have 9-10 hours then I probably won't be taking public transport. I would probably arrange for some sort of private tour who could pick me up at the airport and take me to many sights for the day. I know they have one day tours in Beijing that take you to the Great Wall, Forbidden City and Tiananmen sq. Don't know how I would spend the day in Shanghai. Any suggestions?

It also depends what time of day you arrive and depart.
Are you incorporating an overnight hotel?

But in general, if you have never been to either, I would recommend PEK to see
Forbidden City, Tianamen Sq, Great Wall.

If you have already seen the basics, then Shanghai for more action, things to do.

Shanghai is a bustling fashion capital of China,
and Beijing is a capital of culture, Shanghai will be better.

Beijing or Shanghai on day layover?
 

For a tourist there is no comparison. Beijing offers history and numerous attractions. Shanghai offers tall buildings. Would you rather tell people you saw the forbidden city/Great Wall or tell people you saw some tall buildings? Beijing is the clear winner here.