I think its two schools of thought...Manual or CNC.
I started with manuals and they can do it all, very versatile and your making chips in no time...but you will be tied to the machine. Multiples can be done using quick change tooling...holders can repeat nicely when YOU change them...provided not chips get under the adjusting knobs and stops.
Need to stop a job to run something else...no problem. Grab your chuck key to open up the jaws, reverse or dial in with a 4 jaw. Minutes your running another job.
Need to kinda put a chamfer on the end...bring up your tool and touch, small hand feed and done.
TL is kinda like that...quick, simple versatile. On a manual lathe you may have feed stops so you can walk away from machine and feed stops at the end of a cut. make a 2nd or 3rd roughing cut YOU have to crank handles and carefully come up to your final number. ON a TL, program the cut beginning to end finish pass and machine does it. NICE. Also the TL you can program radius, chamfers, curves and tapers...all doable on a manual...but labor intensive and never quite like a CNC flowing cut going from feature to feature.
Quick change tooling is a plus, change tool and hit go.
Mini turret- nicer yet for multiple operations with no intervention. But usually limited amounts of tooling. AND a TL gets in the way of itself easily. Think clearances...
NOW lets talk CNC lathe.
Chucks are mostly manual adjusting soft jaws that only move a small amount OR Collets which do not adjust. What to change a part size...remove the soft pads, find ones that are close to your size, bolt on, then cut the jaws so the part runs true. That can be 15-20 minutes...plus after so many changes you need new jaws.
Tools on a CNC tend to be generic, you program chamfers...so your not gonna run a quick edge break on a single part or two.
Now the benefits.
You bore the soft jaws or use a collet and your parts run dead on. No more indicating.
Clamp a blank piece in the CNC, set your tooling, program part and you can rough and finish turn, spot, drill bore, thread, groove, cut tapers knurls etc in one setup with no operator intervention...or limited on TIGHT tolerance parts.
Not manually changing tools prevents the wrong tool being put in...prevents chips from getting under stops so tools repeat extremely accurately.
Now perhaps the biggest difference...the enclosure. On a manual you have a pan under to catch chips, catch the coolant. You adjust your speeds and feeds close to the correct speeds and feed as possible. But often with open machines you bring down the speeds of the work turning as the correct speed would make a huge mess. Chips flying all over...if you use coolant that too goes everywhere. No enclosure means speeds and feeds get dialed back.
IN a CNC with enclosure you dial in your numbers and go...plus you get to FLOOD the part and tooling with coolant. Sure coolant is nice to add lubricity so tooling last longer, part size does not change due to heat...BUT the big big plus coolant flushes the chips away. Tools are no longer recutting chips.
Also when tools are programmed at the correct speeds and feeds, they last longer.
If your planning to dabble in turning go TL. If you plan on offering CNC turning go with a CNC. Different machines with a different purpose. I'm CNC but keep a couple manuals as they do different jobs best.