the advantage of chrome lined barrels is that they drop the pressure which the ar-15 is very sensitive to. they also help with extraction of spent cases. the hard chrome lining helps barrels last longer. this is really helpful with some of the somewhat wear prone one in seven inch twist barrels.
lastly they clean up easy.
the disadvantage is they cost a bit more to make.
regular 4140 moly is just a regular barrel steel it will last a long long time with the most often used twist rate on one turn in 9 inches. it has an advantage is it is less difficult to cut the rifling in the 4140 than harder 4150 which makes for slightly better accuracy in theory. without the chrome they are finished a little more rough in the chamber. i have about as many ar-15 types with the 4140 without the chrome and they all function fine.
so the chrome is not a have to thing but it is nice to have IMHO.
stainless steel is also used for barrels. it is usually the most accurate though being a bit softer it wears a bit quicker. it should last plenty long on a sporting rifle.
the nitride is a type of finish --i figure the exterior finish is better--now about the bore i can't say as i haven't owned any nitride barrels. i would not rule it out as being a very good barrel though.
any of these should give years of accurate shots. the one that is best depends on what your use of the firearm is. tack-driver target shooting go with the stainless. survival-military get the chrome lined. all around use the moly or nitrite should do the job well.