I can only speak for OSX, but I've tried a lot of different methods. There are a lot of promising and elegant looking programs that end up having trouble capturing a decent size at 60fps without dropping frames. Or not allow you to change the colour table method and do it based on the first frame only.
There are 3 methods that I've landed on each with different advantages:
Free and handles decent sized 60fps gifs quite well. The interface is a bit clunky. But it's free.
Quicktime + Video editing + Photoshop
Highest quality results (but the most time consuming). Record the entire screen at the highest quality. Frame it and edit it to exactly what you want in Premiere or Final Cut. Export uncompressed video file. Import that into Photoshop and save for web to Gif.
The Photoshop save for web tends to allocate colours really well and get the filesize down. Once upon a time I use to use Fireworks over Photoshop as it had a way better gif export. But I haven't used it in years and can't compare them directly now.
The best complete package i've found (not free: $30 USD). It has replaced both Licecap and Photoshop for me for pretty much every gif I do. It records everything as video and has a bunch of video export options and also a nice gif export. Capture process is smooth, handles decent size at 60fps on my Macbook Pro. Keeps all the source videos stored away in case you want to come back to them . Allows editing after recording. And remembers your export settings. Oh, and it records mouse presses as metadata, so you can export with or without those present. The only caveat I can think of is it doesn't let you choose the recording codec, only the quality. For video recording it would be nice to have the option for uncompressed or Animation codec for capturing clips when making trailers and things. Can be nice having a high quality source stored away for later