IPAs don't age well, or at all. The sooner they're consumed, the better they taste (or taste as intended). Are most of the craft beers you have, IPAs? If so, a "Best by:" would make sense.
Meanwhile, some styles taste better aged, e.g. barleywines, imperial souts, sours. You definitely wouldn't see a "Best by:" for these types, and in fact you might even see a "Best after:". So perhaps the "Born on:" label is a way of letting the enthusiast decide how long to age a beer, without feeling forced to wait a minimum number of months or years.
Would you happen to know or remember the styles (or even better, the exact name) of the beers that said "Best by:" vs. "Born on:"? Then perhaps we could validate or invalidate this explanation.
Interestingly, Anheiser-Busch is the only entity that may use "Born on:", as they've trademarked it.
But anyway, it turns out that another class of beers that typically have production dates are macros (i.e. American Adjunct Lagers), not because they taste better aged, but for a mix of several reasons:
- profit-maximization (purportedly),
- tracking problems and policing freshness,
- giving consumers an (illusory) sense of regulatory safety,
- and giving enthusiasts control over when they'd like to consume a beer.
A Lagunitas employee quoted in the aforementioned link claims that
Bud only really did it to reduce brewery and distributor inventories and wring a one-time load of cash out of the company...
and goes on to say that Lagunitas labels production dates
to track problems [...] and to give our distributors the ability (if they will use it) to police freshness.
A bit biased, but I can believe some elements of both sides.
Furthermore, these threads on BeerAdvocate suggest that some consumers feel better (even might only drink a beer) when a production date is printed, whether it gives them an illusory sense of regulatory safety or they actually know enough about beer to know if and how long to age them.