All welding does is melt 2 (or more) pieces of metal together.
as long as the settings are right you should be able to use either on most steels - the issue with stick / mig welding is the filler is really messy... In most die applications you spend more time grinding the filler down than it takes to weld it.
TIG is a much more controlled and clean process.
best practice is TIG in general.