1st: I'm a HUGE fan of Nebula and have very minor experience with VCC (because I demoed it, but haven't bought it). Take my words with that in mind.
Nebula does an AWESOME job, my mixes are never without console emulation through it. I could go on about this but going back OT, VCC seems to do very pleasing saturation to audio. One thing it does BETTER than Nebula is how it handles transients. Another is that its not nearly as picky about your gain-staging. Now, Nebula's preferences can be altered to provide better transient handling and overall better sound quality at the expense of CPU power. I have yet to compare Nebula and VCC with said altered settings, so I'll refrain from putting any unfounded ideas in your head. Nebula is already pretty CPU-intensive, a big turn-off for many, so this option is only for the Nebula devout haha.
Both Nebula and VCC are pretty subtle, just like the real thing, and both sound great, yet I always wonder about the accuracy of the plugins compared to the real thing. Still, it's not the most important issue to me as the SOUND is my number one concern. Both are much better console emulators than Sonimus Satson or SKNote Stripbus IMO, although they do a commendable job.
Since this is a VCC thread, I don't want to derail into Nebula talk, but maybe someone with both can explain things further