Shipping damage

It depends on who the shipper is.

The dealer.

Few years ago I had speakers delivered by truck "on the
pallet" showing dents in packaging. I could not refuse them
(not enough time) but discovered next day serious damage to one
of them. Shipping/receiving department at my work, where they
been delivered, told me that they came without a pallet. They put
them on the pallet first time when unloading truck to move them on
company floor. I took pictures of the speaker plus box and sent
them to dealer together with the info about pallets. Dealer ordered
new speaker for me. Shipping company supposed to come for
damaged one, but they never had.

Several years ago I ordered a new pair of floor standing speakers from a company out of New York (they are no longer in business). The speakers were shipped UPS and each speaker came in it's own individual packaged box. I accepted the speakers although one box looked like it was droped on the lower corner, and sure enough the bottom rear corner of the speaker was crushed. The company had UPS pick up the damaged speaker and replaced it with no problem with in three days.

UPS is champ in damaging items upto 30% chance.
Fedex has better freight and ground prices and better item handling by FAR.
If you're sending solid unit and not heavy such as piece of 2x4 stud or few, than you're OK with UPS.

One of my first deals here on the gon was for a pair of Talon Raven C speakers to be shipped from Ca. to NY.
One of the speakers was damaged & the crossover became loose.
FedEx sent their claims man to inspect the issue & to make a long story short - I received a refund for the speakers + shipping & was told to keep the speakers.
The damage to the cabinet was very slight & a good friend came over to repair the crossover for free.
Probably the best deal I have ever done here.
Back then (15 yrs.) I had quite a few claims with both FedEx & UPS & got to know the claims guys by their first name.

As long as your dealer is somewhat reputable and willing to process the claim, you should have no problems.

Did you consider asking the shipper whether you could inspect the inner box (your comment of an "outside box" implies there is an inner box) or, if there was only one box then inspect the item itself, prior to refusing the shipment? I have had drivers from UPS or FedEx allow me to do that rather than incurring the hassle of returning possibly undamaged goods to their distribution center. In each case when I inspected the item (I believe only two times) it was undamaged. In a separate instance, a B&W M803 tweeter was damaged and the dealer sent me a new tweeter.

I'm with Czarivey on this one. I've been shipping Vintage Drums via FedEx since 1999 without a single incident of damage. I've received drums shipped UPS, however, with less luck. I pack very well, using multiple layers of bubble wrap rather than the more common plastic peanuts, which simply move out of the way when pushed.

"plastic peanuts, which simply move out of the way when pushed."
+1000 on that, Bdp24. Tightly packed peanuts are good between an inner and outer box, but are totally useless at protecting something that is much denser than they are, which will move "through" the peanuts upon impact. Remember the packing should be sufficient to protect the item from a 6' fall onto concrete.