recessed light only works with halogen bulb?
It may be a dimensional issue. 

Incandescent/halogen typically have a long narrow stem.  CFLs put a pudgy power converter module right at the bottom. Some LEDs unnecessarily do the same since CFLs do.

Often the socket proper is recessed behind a shield or something.  When you're screwing in a CFL, it grabs a couple of threads then the power converter strikes and binds against that shield. It feels like the socket has bottomed out snug, when actually the bottom contacts are not touching.   And the bulb just doesn't turn on!

Check out your fixtures, but I bet that's what is going on.  You can change the fixture, alter the fixture, or shop smartly for long-neck LED "bulbs".  

You probably won't find them in CFL, nor should you look.  CFLs are entirely obsolete. What's more, CFLs are particularly unsuited for aimed PAR lighting since they make a blurry clump of non-directional light which cannot be focused via reflectors or lenses.  LEDs are the ideal case, as they inherently make a cone of light which is easily focused further via optics, which are near 100% efficient.