If you are competitive, you cannot afford to give up the small but real advantages of modern gear. It can easily be the difference between being on the podium or being an also-ran (make that also-pedal). If you are better than your competitiors you can overcome that difference in the lower categories, but once you advance to a level where the competition are your equals, you put yourself at a signifigant disadvantage.
Of course, if you only ride for enjoyment with a little friendly, informal competition, you should be prefectly OK on vintage equipment, as long as you have a strong will to take the verbal needling you will undoubtedly receive.
I would routinely ride my boom era bicycles or an ATB in club races, until advancing age forced me to resort to more modern equipment to erase the disadvantage of the 20-30 year age difference.