I love public courier contracts, they tend to get delivered much faster at lower rates and to/from more places than private contracts through courier corps.
Frequently it is a courier corps or one of their pilots that picks up the public contract anyhow. The difference is the pool of potential courier pilots is vastly larger. Anyone (a member of any courier corps, independent courier pilots or some random player looking to make a little extra for a quick trip in his PvP fit interceptor) can accept and deliver the contract rather than being limited to just a single corp.
As long as you're paying decent rates the contracts tend to get delivered quickly and all without paying exorbitant "rush" fees or much higher rates for trips into low/null.
As an example I've had roughly 350 million worth of Genolution implants sitting at a low sec station in Devoid for a while that I couldn't be bothered flying manually to pick up. That particular pilot is still flying Vigils, has another month or so to go before he can fly Prowlers and I really don't like doing low/null pickups in anything but Blockade Runners now.
So today I set up a contract to move the implants to the nearest high sec station where I could pick them up on autopilot later in relative safety.
The contract was for a 2 jump trip (1 in low sec) and paying 2 million ISK with 350 million ISK collateral.
Then I put the character on autopilot to pickup some stuff elsewhere and tabbed out for a few minutes to do a few things on another character.
Maybe 10 minutes later, I tabbed back in to do the return trip. To my amazement the contract I'd just entered had already been delivered!
Thanks go out to Naskmatar Deliveries for such incredibly quick service!