The core science of diamond growth inside an HPHT cell is essentially the same (a diamond seed, heat, pressure and graphite). There are a lot of variations in the composition of the cell though, which can control color (brown, orange, yellow, blue, colorless, near colorless), as well as overall quality, quantity and size of the diamond.
Outside of the growth cell, the machine and environment also influence growth. Temperature and pressure ranges, tolerances and gradients of the press all factor in to the final quality of the diamond. Ambient room temperature and humidity as well as conditions during the growth cell preparation play a role too.
For consumers though, when considering two 1.0ct G color, VS2 clarity round polished diamonds (for example), it doesn't really matter what process it came from, who grew it or what size or shape the rough diamond was.
Outside of the growth cell, the machine and environment also influence growth. Temperature and pressure ranges, tolerances and gradients of the press all factor in to the final quality of the diamond. Ambient room temperature and humidity as well as conditions during the growth cell preparation play a role too.
For consumers though, when considering two 1.0ct G color, VS2 clarity round polished diamonds (for example), it doesn't really matter what process it came from, who grew it or what size or shape the rough diamond was.