As a private seller, UPS really doesn't want your business - servicing companies is their main business. I know from experience that unless an item is outright lost, getting them to honor an insurance claim for damage is next to impossible because they almost always claim inadequate packing. I prefer USPS but things have changed in recent years. I live in OH and the shipping cost to the different postal zones varies widely. I recently mailed a 13 lb. double boxed airgun and before I listed it for sale, I checked prices for Priority mail to many parts of the continental US on the USPS website. The cheapest was $20 for cities close by and the most expensive was the west cost which was $51. $450 insurance was $6.70 extra no matter where it went. In most cases, ground shipping wasn't even available as an option and even when in was the cost savings was only about $5. Long story short, it makes a huge difference how far away you need to ship.
And a word of advice, great packing is the best insurance. A lot of airguns are pretty heavy and they're pointy on one end. I recently bought an Mrod and although the seller went to a lot of effort padding and double boxing, the gun was able to move inside the inner (factory) box. USPS dropped the box on the barrel end and the barrel poked all the way through BOTH boxes and the barrel shroud was damaged. So it's really important to pad in a way that the gun can't shift inside the box and that you have the end of the barrel heavily padded to prevent if from being a punch.
And by the way, I wouldn't recommend wrapping the factory box in brown paper and mailing it that way - that's just asking for damage. IMO