I've received a lot of questions lately about the various types of lab-created gemstones, and which type is "best". There are many creation types but for the three most common are flame-fusion, hydrothermal, and Czochralski pulled (there are others but these are rarely available to cutters). Flame-fusion is the oldest and least expensive, and is typically used for ruby, sapphire and spinel. Gemstone size is limited to approximately 10 carats, and some colors are difficult to replicate well due to color zoning (blue sapphire is a good examples). Hydrothermal is primarily used for beryl (emerald, aquamarine, morganite, etc) since it mimics their natural growth processes, but gemstone size is limited due to the thin shape of the rough. The hydrothermal technique can also be used for ruby and sapphire, but it's relatively uncommon since other methods offer lower costs, better colors and larger sizes. The Czochralski pulled technique is the primary technique for YAG and alexandrite, but it can be used for ruby and sapphire. The primary advantages of this type are that the color is uniform throughout and that very large gemstones can be cut.
In summary: Hydrothermal: Expensive, best for emeralds and other types of beryl. Limited color range and size.
Czochralski Pulled: Expensive, best for YAG, alexandrite, blue sapphire and/or extremely large stones. Limited color range.
Flame fusion: Inexpensive, available in a wide range of colors, best for ruby, spinel and most colors of sapphire (except for blue - see above).