So far, there's no definite evidence for the superiority of either approach.
For evidence-based medicine, the Cochrane Library is a widely respected source and here's one finding:
link
In detail, the decision is complex as TS&M touches on, but very generally, I'd opt for a laparoscopic procedure for a recurrent or multiple hernia or if there is a compelling reason for a very quick return to full activity. Otherwise, I'd most likely suggest an open approach. Avoiding general anesthesia is a large factor. Being "put to sleep" is, technically and cost-wise, a big deal; e.g. more equipment, drugs, staff expertise, recovery -- just more variables to deal with. As related to complexity, I don't care for that fleeting second or two of initial adjustment to the relatively restricted field and reversed anatomical view (the scope is approaching from behind the hernia). As for cosmetics, final external scarring is a toss-up: an open might leave a single slanting, 6-7cm/2-1/2in scar whereas a lap procedure might leave three little 1cm/1/2in scars (vertically arranged for TEP, horizontally for TAPP).
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p.s. In cases of repeat hernia, the main reason I'd go for a lap procedure is that it usually provides an approach through clean tissue. Basically, the problem is internal scarring ("adhesions") which, in varying degrees, nearly always follows from abdominal surgery or injury. Think of it as being like gluing and sewing tissue layers and vessels and organs together. It can interfere with views; it can obliterate landmarks; it usually requires more and careful work to pick through; it can complicate healing; it sometimes can be just a pain in the arse....