Papa John's was pretty crappy in the US, but I find that it is actually a halfway decent option here in Lima, especially since you can get one for 22 soles including Pepperoni rolls (I always use the Lima Delivery app). You're right that it could use more tomato sauce, but I think they use about the same amount as the Papa John's in the US. As far as I can remember they taste the same, though admittedly I only very rarely ate it in the US (why would I, right?).
Finding a good American style pizza in Lima is difficult. What part of Lima do you live in? There are some okay ones I've come across here and there. Nothing great, though.