In cases pf complex anorectal malformation[high cloacal CC and high vagina location. we open the bladder insert tubes in both ureter to prevent iatrogenic and identification of both ureters during separation of posterior bladder wall from anterior vaginal wall.

where to make the incision ? vertical or horizontal ?

Vertical incision

In small animal species we open orientated parallel with the linea alba / midline (I suspect in your case, this means vertically) because the vascular and neurological structures are paramedian and less likely to be damaged.

I'm interested in whether you think a horizontal incision may offer a benefit, and if so, why?

I am a general surgeon who was trained to do and also used to do some general urological procedures. It is important to state the reason why you want to open the urinary bladder. For example, in open transvesical prostatectomy, still done in parts of the world, and in cystostomies for extraction of large badder stones the vertical incision is easy to do, gives a better access to the inside of the bladder, and heals well. Some surgeons advocates the transverse incision if you are trained to do it, buts it doesnt give as good access as the vertical incision and can easily get lacerated during a more than gentle manipulation.

I recommend vertical incision. I always open bladder by a vertical incision to see the ureteral orifices and bladder neck for any ectopic opening.

I don't remember that I read or do vesicotomy in transverse direction, we usually open the bladder in the Medline vertically, because it is always away from ureters, easily and safely extended, so you can bifid the bladder without risk, though if the bladder is opened by trauma in a transverse direction, it can be sutured in the same direction with the same healing rate.

as well if you need to reimplant ureters, vertical incision will help you more, as you can implant them away from the bladder wound and close to its original site.