Got the OofM bridge removed last night, and snapped some pics for comparison.
The finish is the most obvious difference, with the J-Custom being a bit flatter and smoother. This may be a result of a better powder coat process, or maybe a smoother finish to the metal, or maybe both. The corners of the Overlord bridge are angle cut, while the J-C's are radiused. Corners on the J-C tuner mechanism housing were left square. The saddles are different between the two. Not sure which is closer to the original Steinberger. The string hooks on the OofM are unfinished, while the hooks on the J-C are powder coated. Another obvious difference is the fit. The J-C is much tighter. The tuning knobs barely wiggle at all, while the OofM are all loosey-goosey. The J-C has metal washers under the knobs, where the OofM had those aforementioned nylon thingies, and a much wider gap.
Some differences on the backside include the J-C being sanded to expose a large area for grounding, whereas I had to scrape away finish on the OofM for the ground. The hardware seems more substantial as well. The lock mechanism on the J-C is about twice as thick as the OofM, which seemed to work just fine. The mounting holes lined up perfectly with the existing screw holes from the OofM base. The HeadlessUSA website said that the bridge does not come with mounting hardware, but it did. In fact, it looks to be of better quality than the existing Chinese stuff.
I dug out the stock head piece as well, and took some pics of it compared to the J-Custom part from HeadlessUSA. The stock part is a clamping style like the Floyd Rose locking nuts, and will only accommodate regular strings. The J-C part is slightly larger (maybe 50%), has a better finish, and is designed to accept either regular or double ball strings. The stock part kind of put me off in that if I have to deal with changing one string, I would have to detune the adjacent string using the same clamp. The J-C part has individual internal clamps for each string.
When I strung it back up, I kept having issues with the bottom E string staying in tune. I finally realized that it had started to unravel at the ball end. This was a set of Ernie Ball 9s that came with the kit. I use D'Addario on my other guitars, but didn't seem to have any 9s (had a set of 10s, and a set of 11s, though, neither of which I'll probably ever use). I'll have to make a stop at Guitar Center on the way home tonight and grab a couple sets.
In the mean time, pending the completion of the set-up adjustments, I'ma call this one done.