I breed the lateralis and they are great roaches IMHO. They breed much faster than the dubia and one thing I really love about them is when you drop them in the enclosure, they hit the ground running and running and running, just like the Energizer bunny.
They don't immediately seek shelter like other roaches or crickets will do. They keep looking for a way out. Really attracts the attention of the animals a lot. With that being said, they are fast as lightning and a lazy animal might have trouble catching them, though you can do things like squish their heads to keep them from running all over the place. They also can't climb glass or smooth plastic which is a huge plus in my book.
Lobsters (which I don't have experience with) breed just a bit faster than the Turks, are fast as well, and I believe they also don't go to hide immediately though I might be wrong on that part. The big downside to them is they can climb glass so you have to take extra steps to keep them contained in the enclosure and breeding bins.
Discoids are like smaller versions of Dubia. A little bit faster and smellier than the Dubias, but not too big of a difference from what I have read on them.
I personally am keeping the Turks and Dubia myself, though I plan on adding more species as pets in the near future. The Dubias are great if you only have dragons, as they can eat them from hatchling stage to full grown adults. If you have any smaller animals, then the Turks are nice because they are quite a bit smaller than the Dubias when newly born (almost pinhead cricket size) Also they don't do the hiding/burrowing/standing still like the Dubias so they are a great alternative. Variety in the diet also doesn't hurt, so get both!
