I read up a lot on this before I bought a billet lower, long story short from what I gathered if you're going to beat the crap out of your gun like military in combat go with forged. Everything else billet is good to go. Just make sure it's 7075.
Billet offers other options like built in trigger guard, but now there's forged lowers with a lot of the same options.
Actually, scratch that. It's half dozen one way, 6 the other. Machined parts are machined from a billet that's usually forged. Forged parts are forged into shape and don't take a lot of machining to "clean up".
Personally, I'll stick to the generally cheaper forged parts because outside of "looks cool", I haven't seen anybody show a clear advantage to billet.
My usual pitch on them, having minor experience with both, is that forged is stronger by volume due to the forging process and is cheaper due to the reduced machine time needed to finish them. Billet is more interesting to look at, and is often built thicker in known weak spots in the AR design to resist or at least reduce flexing but is more expensive since there is a increased machine time production component of the pricing. Billet is usually heavier than forged on a per-piece basis.
The strength argument is usually ignored by pointing out that lowers are often found in plastic, with the old Cav Arms system being the strongest (and lightest).
Like many things in life, and especially in the gun world, the difference boils down to personal preference