A simple comparison of the two would be the manual flush would be cycling of trans fluid thru the system via the trans pump from a clean source - not much different than if you did the same yourself in the driveway using a 5 gal bucket as a drain and added fluid until it ran clean.

But the power flush probably works ar a higher PSI, will most likely flush out the torque converter (most trans fluid changes (drain and fill) leave "some" trans fluid in the converter even with the drain plug on most MB trans units. the power machine would most likely get more crap out than the manual method but what PSI is it and can it damage the clutch material? It appears that they want to CYA on damage during removal (man bolts).
Are they getting the trans shipped to thwem or are they a local shop/ What is warranty on damage discovered post flush?
iIhave seen this done on a trans that was crappy but IN SERVICE not a rebuilt unit-think about it...

I'm not a fan of these services but if the trans has been sititng or is a JY unit it may pay to do it but the guys appear to CYS too much.

i would by the trans, install or have it installed, run it for a week or three and see if there is a problem. I would swap the fluid at least once in the first 3 weeks and check for metal frags or clutch material in the fluid before I'd toss $850 into the mix.

I have seen these flush units used as a "premium : add on at some shops as a money generator. when I had the trans in my F150 rebuilt the shop did same a Peter, total tear down and rebuild and manual pump hru cleaning to get any residual material before delivery.

I mean Peter is doing a total rebuil isn't he? Doesn't it fit that he will clean the body and all assorted clutch packs, etc, use a rebult TC that is clean, etc...no reputable shop starts with a dirty shell and rebulds with out a good cleaning...does not make good tech or business sense.

Unless it shows a need for a trans fluid swap or metal/clutch pack material is found I'd take aPasadena...