One maker's barrel is 4140 chrome-moly ...
the other's 4150...is there really any appreciable difference?

4150 steel is harder so it should resist wear better. SHOULD. I bet you would never find a real difference in practical use though.  My dad has some background in metalurgy and when I asked him this question he said "both will last a loooong time, don't worry about it."

.01% more carbon in the alloy.  You'll never notice a difference.  Nor will I.  

Note the terms 4140 and 4150 do not in any way specify or guarantee the complete composition or machining of either of these alloys.  There are many variants which have both standard and private commercial letters to specify differences in the metals.

I believe in rifle barrels both are considered a medium carbon alloy. Both have roughly the same chromium and molybdenum ratio.  I’m not a machinist (my father also is and I have tried to pick up on it for auto-racing applications) but, I believe that the 4150 has a higher carbon content allowing better hardness through heat treatments.

I laughed cause 4WHEELINGUNNER’S father’s response would so imitate my father’s response to such a question. "both will last a loooong time, don't worry about it." Although first, my father would ask; “Why, what are you doing now?”

Rock River 4140
Bushmaster 4150

Note the Mil-Spec REQUIRES 4150 steel be used for the barrels.  4140 is used as a cheaper substitute by most of the Clone makers  (Colt and Bushmaster are the only two that use 4150 and sell to the public - FN uses 4150, but cannot legally sell them to the public).