I've mentioned this on several other threads, so please forgive if you've read this before.
A 4 way toolpost is not slower than a QCTP for most operations. All you have to do is mill the tool body (for an insert type) so that the tip is on centre. then never again do you have to worry about the tool height. ever. change an insert, it's on centre.
For long operations where I use a turning tool, a facing tool, a chamfer tool, then a boring bar, I can put them all in my 4 way and index them as I need them. Yes, it is a picky setup to mill then grind the tools so they are on center, (you only ever do it once) but the superior rigidity and ease of use has me still using my 4 way tool post often.
-- Don't get me wrong, I have an AXA on one lathe and a BXA on the other. they are wonderful. I have tools and situations where I'm happy to swap out the 4 way, and use the Aloris style. When it's good, it is very good! (Yes I have about 20 holders for each tool post)
When I'm turning wood, or doing internal grooving in steel, I use the lantern exclusively. Yes I still use all 3 tool holders. I also find it easier to use small HSS tooling in a lantern.