i ship quilts all across the country on a regular basis- i always send them through the post office- i use priority flat rate boxes when they will fit- when they wont fit i have to use a different box- but i still send priority- with delivery confirmation. I ensure them- if it is over $200 the delivery confirmation is included/no extra charge.
the one time i did not follow this plan the package took 4 months to arrive at it's destination- as long as i've been doing them this way they arrive within 3 days (4 or 5 if a weekend is involved)
i had one package (in over 10 years of sending through the mail) that was damaged in transit- and the quilt was damaged- when i filled out the claim i received the $200 i had it insured for.