Before I praise the product, I have to praise the products support.
I was having problems with the trial version of the software. It connected to my host machine first time without having to mess with any preferences or router settings, I could see my host, but not control it. I emailed support and received a helpful reply three minutes latter. Local time for the developer was 23:30 hours. Did what the developer suggested and my problem was solved (set the remote host to screen sharing, turn off remote management).
In addition to testing JollysFastVNC I also tried Chicken of the VNC 2.1.1. The Chicken would not even let me log into my remote server and gave me a cryptic error message. When I tried the Chicken with a machine on my LAN that I regularly access with built in Screen Sharing I got the same cryptic error. I deleted the Chicken within 5 minutes of installing it. I don't want to waste my time on something like that when JollysFastVNC connected first time, has a plethora of easily accessible settings that makes sense, and support that is there when you need it. Is JollysFastVNC fast? I can't answer that as the Chicken was dead on arrival, and I have yet to compare it with LogMeIn, although LogMeIn has never felt fast in the past.
After my short test I immediately purchased the Home edition that is available on the MacApp store for $10. The difference between home and pro editions is that the home will only store seven hosts, and is meant for non-commercial use. The pro allows unlimited hosts, and commercial use, all other features are the same.
If there is one thing that could be improved it would be the documentation. Adding a short tutorial or list of what settings to use in System Preferences on the remote machine would be very useful, as would a troubleshooting section for dealing with stubborn router settings.