I don't have any data to support this, but I would think that if you only had the minimum number of quarters to qualify, then not working from 62 to FRA would make a moderate sized difference, whereas if you had, let's say, 30 years of credits...it won't impact much at all.
I don't know for certain, but I think percentage-wise, both scenarios would work out the same. IIRC, every year you wait between 62 and your FRA gets you another 7%. And every year you wait, between your FRA and age 70, gets you another 8%.
However, I believe that 7 and 8% are simple interest, and not compounded. So if your benefit at 62 is $1,000/mo, it would be $1,070 at 63, $1,140 at 64, $1,210 at 65, etc.
However, the actual amount is usually higher, because of inflation/COLA adjustments.
With regards to 40 quarters (the bare minimum) vs 30 years though, actually working one extra year probably benefits the bare minimum scenario more than the 30 year scenario, because that one extra year represents a larger percentage of your income history.