The difference, as it relates to barrels, is that 4150 retains its structural strength at higher temperatures than 4140.

4140 is the most common type of steel used for centerfire rifle barrels, because it's a quality steel and plenty strong enough for the job in most cases.  The exception is when the barrel will be subjected to very high temperatures, as often encountered with high-volume full-auto or rapid semi-auto fire.  As the barrel heats up and approaches its structural strength temperature limit, it begins to lose accuracy in a big way, due to increased barrel whip.  Continued fire will often result in a ruptured barrel once the temperature threshold has been crossed.

4150 is required for government weapons because its temperature threshold is several hundred degrees F higher than 4140.  It also holds up a bit better to wear, particularly throat erosion.  These characteristics are considered to be worth the additional material and machining costs, because of how the guns are used.

So, the question is: do YOU need 4150?  The answer is: it depends on how you plan to shoot your rifle, or what your expectations are.  For a target/varmint rifle, 4150 is overkill, as you aren't going to heat the barrel up enough to matter.  For a defensive/combat/action rifle, especially one with a lightweight-profile barrel, where sustained rapid fire is commonplace, I would recommend a 4150 barrel, chrome-lined please.

-Troy

In both cases, the primary focus of these companies is making accurate target rifles.  4140 is perfectly fine for target rifles, as in their intended role, they'll never see the abuse that a duty rifle will.

Both companies have more recently made barrels with lightweight profiles (i.e., M4s), due to the big demand for them that no manufacturer can ignore.  And many folks are buying them as duty/field rifles.  Again, not a problem UNTIL you start doing large volumes of rapid fire.  Only then will there be a difference, but if that's important to you, then get a 4150 barrel.

-Troy