As for the quality of lab-grown diamonds, HPHT has generally been associated with more yellowish and brownish diamonds, while the CVD method is the first to create colourless diamonds. Nowadays, both techniques can produce a colourless and flawless diamond, and there is no difference except the morphology.
It is worth mentioning that information about which method of growing diamonds is better is quite contradicting. However, what is happening behind the scenes is that each company tries to push what benefits them the most. A CVD company will tell their customers to avoid HPHT diamonds and vice versa.