I consider the bow to be a better survival tool, just as I do a knife. As 1 poster has already pointed out, to use your weapon for defense, you've failed to keep a low enough profile (usually but not always).
A defensive weapon, while bugging out, is to buy enough time to make a "quick getaway" OR to get out of a corner so one can make a "quick getaway".
Having a firearm will sometimes get the user to action when they could have stayed still and avoided detection altogether.
As always, much depends on the numbers and level of organization that one is escaping and evading from.
One can learn to make arrows and bows, one can learn to make and sharpen a knife, but one requires a factory for primers, casings, and for most: bullets or molds.
After a major EMP event, the factories probably won't be working for years. Life could, conceivably regress back to the days of swords, armor, and bows,,,for a long time, after the ammo has been used up, including those reloading supplies that are available.
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QMC, USCG (Ret)
The best luck is what you make yourself!