I recently had similar debate to yours, although my debate was between the headphones you own already, the DT880's, and the HD650's.
I attended the So-Cal Head-Fi meet and had a chance to audition quite a few different models. I went in looking to decide between these two cans and came out having decided on.........the HD600's. Let me explain. Ray Samuels happened to have both the DT880's and the HD600's on hand which made a comparison very easy. I had a moderately difficult time finding a pair of HD650's to borrow for comparison, as opposed to the 600's which was the most common Sennheiser headphone in attendance. I set out to discover why this was the case. I believe the setup I used included the SR-71 and Ray's Meridian G08. Considering that you already have the Beyer's, I will focus on the 600's and 650's. The primary and mosty immediately evident difference I found was in the low end. The 650's were impressive in this respect although I had difficulty in focusing on any other character of their sound. In contrast, the 600's were much more balanced and neutral to my ear, although certainly not as neutral as the DT880's. The 880's are TOO neutral for my ears, with a bit too much high end. My personal preference, I must say is towards the Sennheiser sound. The Beyer's did have strenghts in areas that the Senn's were deficient in. I just happen to prefer the overall sound the Senheiser's have. My next choice after the HD600's would also be the Beyer's, alhought the AKG 701's would be seriosly considered as well.
I feel that while presenting a somewhat more neutral sound than the 650's, the 600's also have plenty of bass for my tastes. They seem to be more faithful and accurate to the source. So it comes down to your personal taste in my opinion. Your best bet would be to compare the two at a meet, or buy from one of the sponsors who will allow you to buy both and return one.