I play on a 32" TV @ 1920x1080 over HDMI and what I found with COH2 was there were times when the Videocard/Game identified the TV as a TV and dropped the refresh rate to 24 Hz. And it was amazing how laggy it was. I could tell something to move and it wouldnt move until 2-3 seconds after I told it. The TV would be 60Hz in Windows, then switch to 24Hz in game...puke.
You can force the refresh rate in your Steam startup. Under the steam games properties you will have:
SET LAUNCH OPTIONS
add the line -refresh 60
Ah, interesting. I once tried playing on a large TV and also found it laggy. Nice to know why that probably was.
@orestis97 What device are you using as a monitor?
Rosbone's comment about potential throttling is also worth checking. Sometimes a cable might block a fan on the CPU or video card, and it will throttle down performance to prevent overheating. CPU-Z and RealTemp are likely the most helpful to determine if there's a cooling issue. Of course, you'd probably be seeing similar problems in other games if that were the case.
Are your drivers the latest from their
respective websites? You generally want to avoid using the drivers that come on CD with the hardware, or on the motherboard website, as they easily become out of date.
My signature also has a link to my generic guide for performance issues. Section 2 is probably the most relevant if you feel like working your way through it.