Things I would consider...
How much will I need to bust MDA/DA by?
ILS I'd let it go all the way to autoland.
Non precision, I'd bust by a bit, depending on how close to the centerline the approach was. Given that I have commenced the approach, I'm not expecting the weather to be grossly below min anyway.
Other considerations...
How close is the nearest good alternate? And am i familiar with it?
Are there obstacles/terrain on the approach? Or is it over water?
Ultimately, i want to get on the ground ASAP... I am happy to break rules to do so, but I am not happy to crash in the attempt.