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We use ScreenConnect here, corporate-wide, and it is a very capable product. In addition to the standard desktop use, you can also interact with remote machines using a phone or tablet and that is nice. We have around twenty sites and all are interconnected through leased lines on a private network and we can access all of the manufacturing sites from the corporate office. It saves us a ton of travel.
"They have a consciousness, they have a life, they have a soul! Damn you! Let the rabbits wear glasses! Save our brothers! Can I get an amen?"
I don't use VNC myself, but a few weeks ago the Security Now podcast had a warning that there was some common library shared by just about all VNC implementations that had a bunch of vulnerabilities...so whichever one you settle on, don't get an out of date version...