I have the facility at my workshop a Centauro Beta router mortice/swing chisel machine. We have a Balestrini Pico tenoner to match which is for furniture manufacture as it can only do 50/60mm tenon depth. Tool maximum is the issue.
The setup for both is CNC and very quick both in setup and operating. The tenoner for example once set up you must work of both fences as the machine works in a circuler method of operation non stop, fence can be angled as well and has easy adjustable stops to do both end of rails in two passes. On the morticer the timber stays auto clamped and the chisels head move. The Tenoner can make dowel/square tenons but for ease of making and utilising Morticing on our larger CNC Router or the dedicated CNC Moirticer the speed is the difference. Time is money so to speak. Swing chisels depending on depth may have to do it in more than one pass. The router is faster spinning speed so beats it doing the same matching cut a boon for garden seat rail top and bottom rails morticing. Only issue you do morticing prior to shaping on CNC Router, so it is square, bad point sometimes yo uneed to chisel deeper as it will be shaped of on the CNC Router, way round it is let the CNC router as long as it has the ability to mortice after shaping.
The joints from both machines are push fit and can be so tight you can cause a vacumn when pushed together you must leave a space for glue, when you pull out you get a pop especially on tight grained hardwoods and always a clean finish. The only minus point is you are limited to tenon depth on the tenoner/morticer router as you can only do the replaceable tool tip length even after taking the arising tip out the cutter. Not suitable for larger doors but kitchens or wardrobes or raised panels it is fine. We use it for manufacturing garden benches the back slats with multiple mortices and accuracy was a issue before. This method is fast and accurate so a this problem is no longer an issue plus the advantage of the tenon shoulder being perfect square all the way round as they are machined at same time. We used to use Wadkin Double End Tenoners these can be murder to setup and you must have different runs as you could only do top and bottom in one pass, shoulder sometimes could be slightly out on match, new method is not an issue so very pleasing in assembly.
As I stated you can also do a round tenon on the end of stair spindle, very handy and makes staircase handrails a dawdle as you drill the spacing hole and angle the tenon dowel on the tenoner all very clean and tidy.
So from a production view point it is reliable, fast and accurate. I do not see any issue with what is stronger a round end or a square. The importance is quality of the joint and the end finish. Stress testing both same quality built joints I would think they both compare equally with no negatives concerning either.
