I have all three:
The Chrome lining is said to make accuracy not as good, but for practical shooting, not likely to be noticable. Advantage, said to be slightly easier to clean, and the bore and chamber are corrosion resistant. My Armalite has the chrome lining. To me, I would just as soon have SS.
Stainless is also corrosion resistant, and I note that the very best target barrels are stainless. I note that stainless is corrosion resistant both inside AND outside. Some do not like a shiny finish on stainless barrels, and I agree. But a simple bead blasted finish yields a matte gray which blends well in urban or woods surroundings. My Oly Ultramatch is a tack driver. This is a 1" bull barrel, free floated upper, with a Leupold Vari-X III 6.5-20x, and JP hammer/trigger. Can't make a valid comparison to my other barrels.
Until very recently, I also had a 16" upper with Oly SS bbl, and a 20" Oly Service Match upper. Both were excellent, and no difference in accuracy as compared to my Chrome Moly barrel, which are of similar contour.
Plain unlined Chrome Moly, well, most other firearms on the market seem to do just fine with 4140 Chrome Moly, without chrome lining. And my four CM barrels from J&T and DPMS shoot well, too. I don't have any problems with them, and they clean up as easily as my SS barrel.
None are near a point where I can judge durability, and compare one to another. From what I have read, this greatly depends on how the barrel was treated during its lifetime, heating up in full auto fire (which I does not apply with me), etc.
For a rifle (or any other firearm) to be used in coastal or sea water environment, stainless is the only way to go. Not an opinion, fact. For a general shooter, any of the three, SS, CM, or chrome lined are fine.