Is there a way to convert a VOB to another video format using ffmpeg without sacrificing audio or video quality?
Any time you do any form of format conversion you're likely to end up with some actual quality loss, though if done sensibly you won't be able to detect the quality loss. I do this all the time with tools like Handbrake.
To make life easier, ffmpeg comes with presets to allow you to easily set the options to minimise the detectable loss of quality. Were you to be encoding to x264 then you could use
-vcodec libx264 -vpre lossless_medium for instance.
Your choices will depend on your desired destination format, and what tools you want to use.
MKVToolNix can easily make an MKV out of a VOB. Of course this isn't using ffmpeg (directly? - this kind of stuff is a mystery to me), but it may help you accomplish what you're trying to do.