WARNING - USE UPS FOR SHIPPING RATHER THAN FEDEX

FedEx appears to be slipping again in many key ways including what the OP is talking about. They may say they insure the contents but try filing a claim and having it go quickly with proper reimbursement; that's another thing altogether!. In addition their tracking systems don't show updates for hours and sometimes more than a 1-2 days at a time in the case of a problem. If they have a weather or mechanical delay the tracking simply 'stops' and shows the package in its last state or depot location before the problem occurred. This has happened 3 times in my last 3 shipments with them over the past month alone.  Their customer service reps have no better visibility than what we have on the public website either and the litany of apologies is long and frustrating.  

UPS on the other hand is much better at showing location/status of a given package but is reportedly very difficult in extracting payment for the exorbitantly priced "replacement value" shipment insurance (at least $2.49 USD per $100 valuation over the first $100).  There are countless stories out there of difficulties proving the case and getting money back.  
I've had a number of shipments with both over the years where I was forced to contact Esoteric, Classe, Edge, etc...and buy, out of my own pocket, replacement shipping cartons. There seems to be no way to get a shipment across with the peace of mind of it looking decent when it arrived as a guarantee. It's good the contents make it intact but these shipping cartons are not inexpensive, often costing $100-$300 or more per set.

The only way I've seen to ensure both FedEx and UPS do a good job overall is to pay the very high additional shipping charges for at least "Standard Overnight" (Next Day Saver often gets less quality handling) or "Priority Overnight"/"Early A.M." levels of service.

As an aside,...for high-value electronics, I was pointed to SBA ("Service By Air") by Esoteric and BAX Global. I've used SBA several times and their quality is first rate. BAX is reported by some friends as being 1st rate as well, particularly for super large amp, speaker and other high-end shipments.

By far the most informative and helpful post in this discussion, from which hopefully all will benefit.  

I just obtained a quote from SBA on an expensive item I'm about to ship.  The representative is a local person, who I can look to and trust to resolve any issues whatsoever - much more reliable than contacting a "no-name" in a call center somewhere, who is not accountable for the company's failure.  

Sure... it may be a little more costly than UPS or FedEx... but... not much... and... that is a small price for the assurance that a multi-thousand dollar piece of equipment will be shipped with utmost care and will be reimbursed timely if damaged in shipment.  

While FedEx and UPS may be OK, for low value items...  No doubt SBA is a much safer way to ship expensive audio equipment, which is heavy and bulky.    

 Fed-Ex uses independent drivers and in my area they all look like the truck broke down up the street and they had to work on it getting all dirty for a few before bring my package. Not a  good look..Ive actually seen a fed ex driver open his side door and push my Rel sub out the door with his foot out onto the sidewalk.Telling me as I ran out my front door  up to the truck "boy thats a heavy package"...now UPS in my experience fights any and all damage claims no matter what.I guess thats par for the course as insurance is a rip off game anyway.They will come up with any excuse not to pay for damaged items....so its all a gamble when shipping with either