Although you did mention a LAN environment, I'll still add the following: You can not take your desktop with you to your iPad, etc; no remote access is available like with VDI (I use my iPad in conference rooms inside my office building quite often). You can't give external vendors desktops like with VDI. You can't have users work from home occassionally; OS streaming will not work there. VDI will.
OS streaming means you're still powering up your power-hungry old machines instead of leaner, more energy efficient zero or thin clients.
For remote offices, you'll need to put a separate provisioning server setup in each location. Why? Let's use the example Citrix themselves gives: If you have 50 remote users using Vista with a 100Mbps link, it will take 13.5 minutes for them to boot up. You need a solid network with solid speeds to really utilize OS streaming. You can get away with much less using VDI and the multiple protocols available.
For BYOPC environments, giving a user a virtual desktop and pointing them to your portal is must easier than helping them set up their laptop or desktop to use OS streaming (if it will even work).
Blog: http://blog.eeg3.net