I have the same problem. I've been using Capture One Pro for over a year but have decided to give Lightroom a try. In Capture One, my exported sRGB images look fine in Windows Explorer (not color managed, but they look as expected), and in Picasa and Firefox (also not color managed, but again, they look darn close to Capture One's display). Of course they all look fine in Photoshop, which is color managed.
Exported sRGB images from Lightroom, though, look washed out in Explorer, Picasa, and Firefox, though they do look as expected in PS.