From my experience working in the Facilities department of a few large buildings, white would be more efficient. It all depends on where you are, costs of utilities, what utilities you use for what, etc., but generally heating costs less than cooling.

For example, in our main building we have four large Trane Intellipak HVAC units (and a smaller Trane Voyager unit for the lobby). These suckers are the size of semi-truck trailers, and have six AC compressors, each.

Running just one of those to cool the supply air (what gets shoved down into the building's ducts) to 65F (pretty cold, but it could go all the way down to 45F before we risk freezing up coils) takes more power because of those compressors and the fans that would have to run, than having all four units heating the entire building. Thus why we have a white roof on each of our buildings.

The reason for this is how our building is designed: We have a large boiler which pumps hot water into conduits that run along the perimeter of the building, into radiators within some of the ducts, which then heats up the air, and blasts it out around the inside of the perimeter of the building. Air then gets sucked up into the return ducts located towards the center of the building. In this configuration, we just run the boiler, and each of the large units does minimal heating, instead just running their fans to push and suck air. Plus we have enough insulation that the building doesn't get too cold at night, and the units maintain the temperature overnight to a comfortable, but cool, temperature. In the morning, they roast the building (because everyone complains how cold it is outside, and they want heat inside, etc.) and then let the temperature settle until the sun can help heat the brick walls.

In the summer though, because of how much electricity those compressors suck up (and the fact that our IT admin, and each tenant's IT admin, likes to run their server rooms at 65F, causing the compressor for each server room to almost constantly run), we have to take aggressive anti-waste policies, like shutting off lights in the hallways, reducing from 32W to 28W fluorescent bulbs, and turning off 2/3 lights in office spaces (each desk has task lighting or a large floor-to-ceiling window). It's paid off though; we're now LEED certified, and have reduced electrical usage by about 20%, bumping us down a pricing tier for our local electric provider.

One thing that a lot of people don't factor in is the cost of maintenance of these roofs. For example, here in the Sacramento valley we get a lot of pollen, dust, and smog from San Francisco. Once per year, we have to take a pressure washer onto the roof of each building and spend a few months cleaning all the dust and dirt off each one. Imagine your car during pollen season not getting washed for a few weeks... Now with tens of thousands of square feet.

tl;dr: White is generally cheaper, because it's usually cheaper to heat than cool a building. YMMV depending on location, heating/cooling costs, utility rebates, and dozens of other factors.