The return=Lw== is just going to your home page, the other sites are redirecting to a different page. The redirection shouldn't be causing the slow down. The version numbers are also not the issue. The main component had some fixes to increase it's version to v5.1.2. Most of the profile plugins haven't had to be updated since release, so they are still on v5.1.0.
As for JomSocial being slower, it could be communication with Facebook in general. We do a separate request to Facebook for the user's avatar, all of their profile information, and their current status. If you try disabling some of those things, you can test to see if there's a speedup. Honestly, it shouldn't make a huge difference as Facebook is very fast, and your server should be able to make those requests pretty fast as well, but it's a good test to run.
One thing you can do is set the "Enable Debug Mode" setting to "Yes" and see if any additional messages show up during logging in. Those may provide some clues if JFBConnect detects issues.
We do have plans to reduce the queries to Facebook (and other social providers) in future releases, but those will only provide very incremental speed improvements as requests still need to be made from your server.
I hope that helps explain, but if you narrow anything down further, just let me know.
Thanks,
Alex
Slow login process compare 4 sites 2 slow and 2 are okay
