I'll start right out by saying that NOx production is very sensitive to engine tuning, as VW has shown. If you run lean you increase your mileage, but you run hot which can increase your NOx output by two-digit factors.
I scanned the literature real quick, and it's pretty mixed. I think stuff before the ULSD switchover pretty clearly favored the biodiesel, because No.1/No.2 were nasty. After the switchover, with a properly tuned engine, it seems to be pretty close with the ULSD having perhaps a slight edge. Without retuning the ULSD seems to be somewhat better. However all of this varies pretty broadly - some people found improved NOx levels just from switching biodiesel. I didn't find a good, modern paper that quantifies the increase, a few looked promising but were paywalled.
http://umexpert.um.edu.my/file/publication/00003184_92278.pd...
I thought this was a good summary of the effects of biodiesel and tuning strategies on various engines. Like ethanol vs gasoline, biodiesel contains more oxygen than its fossil counterpart. It's also not as fully saturated. As such it just tends to run leaner and hotter, and that's why there's a change in average levels. There seems to be a huge variance in the data. Some possible explanations: every manufacturer tunes their engine a little differently, air conditions like humidity and altitude may play a part, and the composition of the biodiesel may not be constant (eg percentage of fossil mixed in, level of saturation in the feedstock, different additive mixtures, etc).
I think manufacturers probably tune their engines primarily for fossil, and to improve mileage they tend to run them as lean as emissions standards will let them get away with. So they may be fairly sensitive to small changes. It would probably be best to add biodiesel to the emissions tests as well, to get them to pay some attention to tuning for it. Maybe there's a happy medium that will work acceptably with both. If not - flex-fuel ethanol vehicles are capable of automatically detecting the level of ethanol and adjusting their tuning to match, we should have something like that for biodiesel. Perhaps a property like acidity or density, levels of particulates, or presence of a taggant in the fuel.
Anyway, hadn't looked at that stuff since before ULSD was out and didn't realize it had changed the picture a little bit. I don't mean to minimize the problem, acid rain sucks and we should absolutely do what we can to address it. But there's no zero-harm solution, if the increase can be mitigated or kept minor with proper tuning there are some compelling benefits to biodiesel over fossil diesel.