just a note: forging does not make the metal denser. However, as mentioned, the mechanical properties are very much inproved over casting.
Applications that require high strength and good fatigue resistance are forged (generally speaking). Aircraft engine parts that rotate are forged (blades, rotating seals, and disks), although some turbine blades are single crystal "grown".
If the application involves having the part spend the majority of its life in a highly stressed condition, with stresses as a large percentage of yield, then forging is the only way to go. Cast parts are (again, generally) susceptible to failure by cracking, with the crack unzipping the part leading to catastophic failure.
Don't mean to scare anyone, but jet engines fly around all the time with cracks in the critical parts. However, the cracks are small, and their growth rate is understood, and these parts are "life limited" in that they are replaced on a set schedule. The air force gets a lot longer life out of jet engines by having spent the money to understand when particular parts are likely to develope cracks, and how long the cracks can be allowed to grow to and still provide safe operation.
Cast parts are used where the stresses (or cycles) are low because they can be substantially cheaper to manufacture than forgings, due to casting close to final shape, reducing or even eliminating the machine-to-finish-shape steps.
For an AR lower, cast is problably okay, the part sees little stress (I mean, it IS aluminum in the first place, right?), but most people prefer forged for the sense of (maybe misplaced) security.
Think about it, they make the lowers out of carbon fiber too, right? And the matrix there is epoxy, which is about as brittle as it comes. This is possible because the stress (and the zero-to-max stress cycles) for these parts does not come close to the expected fatigue failure life for the design.