I've done quite a bit of research on LED's in signage, but confess have never installed or worked on one. They're just not that popular. I can see them being used in signs for edge lighting and like Larry mentioned, small channel letters that just don't lend themselves to neon. They make great message centers. And scoreboards.
I may be a bit prejudiced, having spent most of my life in neon related work, but I do have some problems with LED lighting, the biggest one being the claims made by a lot of LED manufacturers when comparing to neon. Without going into detail, the false claims run the gamut and include longevity, energy efficiency, and brightness. Other problems - Some manufacturers will not allow local supply houses to stock their product, possibly prolonging a sign's down time. At the last major electric sign show in Las Vegas, I'm told 27 different LED manufacturers were represented. As it stands right now, none of the modules are interchangeable. Supply houses are definitely not going to stock 27 different brands that may or may not be in business next year. This may be nothing more than the LED industry "growing up". But as of right now, it is not standardized.
LED outline lighting, or border tubing (a string of modules encased in a flexible plastic tube), leaves a lot to be desired. I've seen this application, and I've quoted LED border tubing. At least 2x as expensive as neon, not near as bright, and not near as flexible (if you can draw it with a pencil, we can make it with neon).