I can't answer about Edgecast, I'm not familiar with their services, but generally speaking on the benefits of good Content Delivery Network (CDN), I can address.
The benefits will of course be dependent on your situation— how much web traffic does your site get; how much of your data can be cached; what systems do you have in place if your server goes down; how sure are you on your site and ISP security; how much memory is allocated to PHP, Ruby, Python or whatever program language your using; as well as how much memory does your database and other server resources have access to.
Note/Disclaimer. My experience is based on using CloudFlare CDN services. Our clients are primarily nonprofits and generally affording a CDN is out of their reach. But the free options of CloudFlare do way more than what we as web developers could do.
Speed. Speed is the biggest benefit of most CDN networks. If you've optimized your site as much as you know how to, but still experience slow downs, or just if you've never bothered to test for mobile or modem speed devices. A CDN can greatly accelerate the delivery of your content to the most important people (the users). Your site could be 50 pages or 50,000 pages and this would still benefit users. The difference between millisecond load times versus 2, 3, or 5 second load times can be excruciating. They accomplish this by a combination of minifying, caching, and serving from different servers.
Security. We had a client who was getting plagued by bots. Some were possible spam harvesters, but many were legitimate search bots with absolutely horrendous crawl patterns. They were hitting areas that we specified as Don't Index, since they had known crawl issues, like our tags and search areas, where you can just keep adding keyword and after keyword after keyword. They were bring the server to a crawl, taking up all the resources allocated.
We literally kept throwing more and more resources, going through three memory upgrades, combined with a really hardcore .htaccess file that block and disallowed everything with can find. We used Perishable Press .htaccess references and blacklist as a starting point and kept building. It was untenable, sometimes the site would zip (when the bots were resting) then it would slow to an unresponsive crawl for hours on end. Adding the site to a CDN (CloudFlare) over the weekend, made immediate improvements. The weeded out the bad from the good, enforced our rules, and limited things I don't even know, and in general return the client's site to consistent page loads under 1-2 seconds. This site is very database heavy, so that was extremely important.
Spreading the Wealth. The other great benefit from using the CDN was that it delivered pages from nearby servers, whenever possible. The US like Australia is a big country. Access from New York to a server in California can add time to page loads, just with network latency. It's not perfect, but the CDN allows east coasters to access from New York or DC passage ways, west coasters to access California or Arizona passages, and the midwest via Minnesota, etc.
We haven't tested on every client, but on the ones were we knew it was important, we saw static file sizes drop dramatically, and this is with the original file staying the same. The compression happens on the cached copy which is then also served from the closest servers possible to the user.
So those are some of the most beneficial things we received for our clients, 90% of them who are on a free CDN account on CloudFlare. We've encouraged purchase accounts to gain access to more rules (to bypass certain folders, content types) and to increase security for a few clients and even those rates are affordable for our nonprofits.
The benefits for you will vary, but I think, speed, security and minifying carry over across the board regardless of the CDN or the website. The price for a good CDN can be very expensive, which is why we're very happy with the new bread of small business and individual user focused CDNs.
CloudFlare has resources highly concentrated in the United States and Europe, see Resource Map. But they do have some delivery centers in Australia, but I'd assume if Edgecast is Australian based that they would beat them out in terms of coverage. Their blog is a great resource for optimization tips, understanding networks and security. They recently had a good article on pushing Nginx to the max.
I'd say if you're looking to see if you can benefit from a CDN, there's no harm in giving a free service a try. It's very easy to add and remove. If you find it beneficial but want more specialized services or just closer services, then you know that a local vendor maybe the way to go.