The .411 Hawk is part of the whole Hawk/Scovill family of cartridges which are based on blown out '06 and 9.3x62mm Mauser cases. It offers a very efficient cartridge that will fit any 30'06 length action with few modifications, and easily produce 4000+ftlbs using smaller powder charges than most .40+ cal rifles.
Bullet selection is quite limited in .411, even more so than .416. Hawk, Barnes and a few custom low volume places make .411 Bullets of various configs, and there are cast lead bullets of suitable weight and shapes. The .41 Mag bullets may work for low velocity loads, but few are intended to hold together at the type of velocities that the .411 Hawk or .411 KDF is capable of driving them at.
The .416 bore offers many more choices in terms of bullet selection. Barnes, Swift, Hawk, Kodiak, Nosler, Hornady, Woodleigh offer factory .416's designed to operate in the range of velocities offered by the .416 Rem, Rigby, and Taylor. Cast bullets are also an option for lighter game and practice, although some jacketed bullets will do just fine on game lighter than Cape Buffalo or Kodiak bears. I've seen a Speer SP bullet from a .416 Rigby Ruger #1 pole-axe a deer from ~125 yds. It didn't take 2 steps after being hit. This was from a reduced load (for a Rigby) traveling at velocities easily met by the extremely efficient .416 Taylor (.458 Win Mag necked to .416). I plan on throwing together a Taylor as soon as I find an affordable Mauser action and barrel.