I generally rent rifles on these kinds of trips, but not necessarily due to it being cheaper. Often it is not as you just need pay excess baggage fees to bring your own. Some countries may have a rifle import fee too, but I think generally it is just a wash from a cost perspective.

I rent because the last thing I want to have happen is have the airlines damage one of mine, let alone have one stolen in a foreign country. I have not heard of that happening, but it crosses my mind. Not having to roll the dice concerning how big of a PIA firearm control is going to be is another reason.