Without accepting the premise that the two types of killing cause equal pain and it is only if the slaughter is done badly that there is a problem the slaughter is more likely to be done badly with religious slaughter. Training people to do religious slaughter well is harder than training them to do other kinds of slaughter. In particular, the latter is more mechanized, so as long as the equipment is properly maintained many problems can be avoided. Religious slaughter is much more prone to human error.  It will be much easier to teach people best practice and improve animal welfare if we require them to use the simpler methods, where less training is required. This is a more efficient way of improving animal welfare than studying a myriad of different types of knife etc.