The vintage road bike will let you run something a bit closer to a real cross bike (drop bars, 700C wheel/tires, etc) and be a bit lighter than a mtn bike. But, but the time you rehab it, add tires, etc, you'll be at least $100 in, possibly more - I'd put that money in a jar for a real cross bike next season.
Mtn bikes are legal in everything but the top UCI classes. Just remove any bar ends (required to be removed) and anything else for weight (bottle cages, saddle bag, etc). Add some narrower tires and go have fun. The mtn bike might be heavier and harder to shoulder (smaller main triangle), but other than that, it's fine. Lock out the fork, or at least crank up the compression.