I have a lantern type tool holder on my 12X37, along with a 4-way and an AXA QCTP.
4-way: I have tooled the 4 way for normal turning, parting and facing without any shims or mods. For insert tooling, it is much faster than QCTP, but limited to the three basic functions. I use it surprisingly often. (I suppose I could put a chamfer tool in the 4th position, but never got around to it) this is also the most rigid of the three tool holders.
AXA QCTP: I only bought it last year after over 30 years of machining. I had heard bad things about QCTP from my mentor (he still only has 4 way). All the things were untrue biases. That being said, I find QCTP enjoyable and functional. If I had only one system, AXA QCTP would be it.
Lantern: This is the black sheep, but surprisingly I come back to this quite often. I am in the process of upgrading my lathe, and will miss this versatile (but flimsy) tool holder!! It is boss for home ground 1/4" HSS turning tools, and lets me reach around things the others can't. When I upgrade, I will be sure to find a way to put a lantern tool post on the new lathe. BTW my parting tool in the lantern mount is just as secure as my AXA, go figure (!!). (that is, it chatters very little on normal parting)