O yea, wired half a second. Wireless 2.5 minutes. Powerline 30 seconds. To be honest, I've had wireless performing better than the powerline adapters. It all depends on the building's wiring.
Yes, it should be much faster and better looking. LogMeIn uses the Internet. While with Remote Desktop, you'd be using local area network. LMI is limited by your internet Upload Speed which on average is around 1 Megabit. With a wireless N router, you can can get up to 300 Megabits. You could enable LAN Speed Experience under Remote Desktop which will look and feel just like a regular Windows 7 Installation. Furthermore, if the Internet were to go down, you would still be operational since you cut the Internet out of the equation. I still have no idea why people use LMI in their offices.
How pressed for space are you? Mini ITX computers can be mounted on the back of monitors. About the size of two reams of paper. Since you already have the computers, no point in me telling you that, but just for future reference.