In my opinion, as a shoe/bootmaker...for the life of the shoe... a half sole is indeed a better solution when pegs are used to secure the waist. But that isn't always an option. The sliced joint on a half sole will generally be the weakest connection and may come loose before the half sole is worn through. Sometimes that can be a real issue, fraught with real danger, such as in the saddle.
75 years ago...thereabouts...half soles would have been done with press cement and presses...even, esp., in shoe repair shops. This made for a very strong bond. But nowadays everyone relies on neoprene based cements and these can and do come loose. Oxidation, chemicals, UV take their toll.
If the shoe is sewn from the breast of the heels to the breast of the heel, a "3/4" sole --the slice being placed under the breast of the heel--is the better/best solution. For many of the same reasons mentioned above...the unreliability of the splice, for example.
Topy would have been fine but to do it right...to protect the mechanical and functional integrity of the shoe...the Topy needs to be either put on when the shoe is made or immediately upon purchase. As a replacement/cover for a worn outsole...as substitute for a half sole, IOW...it leaves a lot to be desired and introduces factors that are more problematic than beneficial.
On edit...the one thing that is too often overlooked, even by "professional" shops or makers doing after market repairs, is that the splice between the new half sole and the existing waist remnant must be precise--the transition smooth with no lumps or changes in thickness. It is all too easy to inadvertently put a "met bar" (a orthopedic correction) on an otherwise normal shoe through inattention to this transition.
Edited by DWFII - 3/16/14 at 11:09am