Had bad experiences with both, so I'm unsure too. Almost all local mechanics (ustaads) prefer and recommend option 2, but not only it is time consuming, if done incorrectly or in haste, it may distort the tyre and make it useless. This has happened to me at least twice.
This does not mean the 1st one is better. It may also lead to a loss of tyre, as I have experienced that too, though maybe this risk is lower here. The good thing is you don't waste too much time, so I usually go for that.
I guess it also depends where the puncture is i.e. on the tyre front or sidewall, but experts here can shed more light on the preferred option.