Examine both methods.but tyre shops tell me its a temporary fix and to get it to a permanent fix they need to take the tyre off the rim and patch it from inside.
Now are these tyre shops talking from experience or from loss of business?
The inside patch costs more to install. And it can create an unbalanced condition unless the shop charges you for, and does, a proper rebalance after the inside patch has been installed.
The inside patch will not hold air any better than the properly installed plug will. (Zero leaks). And at the same time does not require the wheel to be removed from the car, and the tire to be removed from the rim. Nor is any rebalancing required after it is installed.
You make the call.