Hello, and welcome to Headfi!
Whether you'll find the Omega IIs better than the HD650s is up to your ears. Having owned the Omega IIs for about a year previously and having spent some time building a system up around the HD650s myself lately, I would have to say that in terms of musical enjoyment, the move up to the Omega IIs probably wouldn't be worth it money-wise.
They have very similar characteristics...they're both a little "dark" in the mid-treble region, have a very smooth, lush midrange, and powerful bass response. The major difference is that the Omega IIs are much,
much more transparent and detailed, and thus is very highly dependant on the rest of your system to sound good. If you never believed in cables making a difference before, get ready to audition cable after cable with the Omega IIs...it can literally make or break their sound. The HD650s are a little more forgiving both on the music and on the equipment. The other big difference is bass...the HD650s have a very high impacting bass that you can really feel, the Omega IIs have a very accurate, deep, and powerful bass response but you can hardly feel the bass, it's a "weakness" of electrostatics.
If you get the Omega IIs, just get ready to change other parts of your system as the Omega IIs WILL show off the strengths and FLAWS of your current system. Getting the Omega IIs certainly didn't end up upgrading.