When comparing Remote Desktop Connection vs LogMeIn, the Slant community recommends LogMeIn for most people. In the question“What are the best ways to share your screen with others?” LogMeIn is ranked 6th while Remote Desktop Connection is ranked 10th. The most important reason people chose LogMeIn is:
You can access a computer that you've previously installed LogMeIn on from any computer that has an internet connection through their browser. There is nothing to install on the computer you are accessing from.
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Pros
Pro Part of Windows
If you're on Windows XP or later, Remote Desktop Connection is already installed on your machine.
Pro Cross-platform
Works on Windows, OS X, iOS and Android.
Pro Access through a website
You can access a computer that you've previously installed LogMeIn on from any computer that has an internet connection through their browser. There is nothing to install on the computer you are accessing from.
Pro Easy setup
To set up, you need to create an account on LogMeIn, download and run their software on the computer you wish to be able to access, and set the software to allow accessing that computer from the Internet.
Cons
Con Not available in the Home edition (only as clients)
Con It's not for screen sharing, but for remote management
Microsoft Remote Desktop is developed for mostly enterprise users for remote control, not to share the screen with a friend. It lacks firewall support, and is much more complicated to setup properly than some other apps, designed for fast and easy sharing.
Con Not free
There are other programs that do the same and are free.
Con The sound and chat can be buggy
The quality of the sound and chat is fairly inconsistent.