I've owned both the Modi/Magni & the ODAC/O2. You can't go wrong with either... especially for the HD600.
The O2 is battery-operable so the OBJ stack transportable. The O2 has two gain settings, enabling it to drive sensitive IEMs more smoothly (than the Magni which has a fixed, fairly high gain setting). In terms of driveability, the Magni & O2 have plenty of power to feed the HD600. That being said, the HD600 sounded a bit more robust, effortless, and rich via the Magni. With relatively sensitive, high impedance (full sized) phones, I preferred the Magni to the O2... though both drove said phones with an impressive degree of refinement and control. I believe the Magni outputs ~1W, so it's got plenty of juice to drive many of the popular orthos, as well (i.e. if you fancy the HE-400 or something down the line).
The Modi & ODAC were very close to each other in terms of performance. I did a lot of A/Bing between the two (using both the Magni & O2) and found I preferred the ODAC to the Modi. The ODAC possessed (slightly) better resolving ability, tonal accuracy, & more pinpoint imaging. Again, though they were very very close.. and my comparisons weren't double blind or anything... purely subjective, too.
Aesthetics is a no-brainer: the M/M stack looks incredibly clean and stylish vs the more utilitarian OBJ stack. The new (C5) case that the (JDSLabs) ODAC comes in is terrific, though. It's much more professional and better built than any of their prior enclosures for the ODAC (and c421, etc.).
If you planned to use the HD600 primarily with this rig & aren't terribly obsessed with uniform aesthetics, I'd go for the an ODAC+Magni stack if I were you. JDS might even offer the (RCA) ODAC in a silver case (which should be very close to matching the color of the silver Magni). Grab a Magni off the FS forum and it'll help offset the (premium) cost of the ODAC (over the Modi).