Both are good and functional. It probably boils down to preference, at the end of the day.
Bit holder:
+uses cheaper 1" bits
+over time, you'll probably acquire bit sets that include a bunch of 1" bits, so there's a good place to use them
+for obscure bit sizes, like Torx 15, you probably won't bother getting long ones, so this is what you'll need
+you'll occasionally need to stick the 1" bit directly in the nose (because of a lack of room), so having short bits around is useful
-bit holders that aren't 'impact ready' can break in time. For a couple of bucks, you'll replace it. Eventually, you'll lose your mind and buy something like a Wera Rapidaptor for $25 or so.
-a tiny bit more wobbly than a direct bit
Impact-ready bits:
+a little bigger and harder to lose in your pockets
+if you buy 3" long ones, they'll interchange with your Picquic screwdriver
+(edited in, following comments) a longer bit will sometimes let you get into a tight spot or sink a screw more deeply than the bit holder
-a little more expensive, and heartbreaking when they break. (And they will. At the least convenient time possible.)
I'd try to join one of your existing bits to a 1/4" socket. Maybe the slot will fit nicely into the 1/4" drive side of the socket? A bit of file work should get you to something pretty firm. Then apply liberal amounts of 2 part epoxy and you should be good. (Bonus if you can find a thin rare earth magnet to sit in the bottom of the socket to hold your bits better.)
Best Answer
Impact (or hammer depending on your region) drivers have a locking mechanism which holds the bit in place:
Usually the drill bit will just snap right in. To remove it you need to pull the collar forward and the bit will pop out.
Typically you would buy impact-grade bits such this one which are designed to twist at a specially designed weak point so that the phillips end does not fail and break.
A hammer drill is typically used to drill holes in concrete as it exerts a hammering action to break up the material which it drills into.
You can get a dedicated hammer drill or lots of standard drills have a hammer option (not as effective as a dedicated hammer drill but good enough for small-ish holes).
An impact driver does not exert a hammering action. This can be confusing depending on the terminology in your region.
Not to be confused with an impact wrench which natively accepts sockets for automotive work.
Milwaukee also produces a 6 inch locking bit extension which will hold the bit in place using the same principle as the impact driver's collar:
So you could attach this to a regular drill and always have the convenience of a locking collar for quick bit changes.