I always have wondered what was the reason for the differences in light output of soft white, frost and clear light bulbs. If I wanted the most light output out of fixture that is covered would it be better to use soft white or clear? Thanks.

Biggest light output in all cases give the clear lamp.
So if the fixture and/or application does not need coated lamp, use the clear one.
But this is valid, when lamps are identical otherwise.
The coating/frosting consume only few percent of light, way more may be very easily lost with inferior made (cheepeese) or wrongly rated lamp (130V lamp on 120V mains, 240V lamp on 230V mains and so on)

I always have wondered what was the reason for the differences in light output of soft white, frost and clear light bulbs. If I wanted the most light output out of fixture that is covered would it be better to use soft white or clear? Thanks.

As far as I can tell from catalog, there is very little difference between clear vs coated

Clear bulbs definitely produce more glare, but they intensify the shine of glassware and flatware, which is why they're used in chandeliers and dining room lighting. 

Clear glass is also a part of decora in these applications. White bulbs would just look weird in chandeliers.

Clear bulbs usually cost more and they're usually not sold in 4, 8 or 12 packs like mass produced frosted/soft white type. 

Manufacturers are not always very honest in their lumen claims for different incandescent lamp coatings, but basically the following are typical figures for the four different kinds of finish:
Clear = 100%
Inside Frost = >99%
Satin / thin internal coating = ca. 95%
Soft White / opal / thick internal coating = ca. 90%