AWS isn't that hard to configure. ElasticFox puts a nice GUI to it and while it will take a short while to get used to the AWS way of doing things, you're better off.
With AWS, you have a nice spray files everywhere storage in S3, EC2 provides lots of RAM and CPU muscle, EBS provides RAID-level reliable persistent storage for EC2 that can be backed up to multiple data centers with a single API call, CloudFront even gives you the chance to have static files served from 12 different locations in the world making your latency very small. If you need more servers, no problem just wait a few minutes for them to boot. If you need more bandwith, it's automatic. If you need more storage, S3 is infinite and EBS can always give you more (you can even stripe the drives so that you could have terrabyte after terrabyte of storage as a single drive).
Dedicated servers have little upside. You're relying on physical hardware in a very acute fashion. While AWS runs on real hardware, there's an abstraction level which helps a lot. Let's say you're small and want a single box. That box fails, you call your host and get a new one in a couple hours, you restore from backups for another couple hours maybe and you're back online. Of course, many often don't test their disaster recovery scenarios that well and are often met with little problems. With AWS, you simply boot another machine off that image and you're good. Worst case, your EBS gets trashed and you say, "hey, S3, rebuild that EBS drive". Easy by comparison.
Real boxes are a pain. You have to deal with RAID, backups, how fast your company can provision new boxes, bleh! AWS (or even Slicehost and Linode) isolate you from a lot of that mess. There's a reason virtualization is the hot new topic.
AWS isn't that hard to use. It's definitely different, but it makes so many other things so much less painful. If you want some of the benefits of AWS with a "simple as dedicated" feel, try Slicehost. You can get instances with as much as 15.5GB of RAM and they just give you the instance with your choice of Linux on it. From there, you can install Apache, MySQL, other. And you get benefits like cheap and easy backups - they just store an image of the machine. Then, if you need more capacity, you can boot one of those images as a new instance, now you have another server. If one of their servers fails, they can easily migrate your instance to another box. RAID10 is already set up. Easy.
If you're worried about AWS' management being a little different, don't worry too much. It's not that bad once you start using it - just a tad hard to imagine without trying it. If you're still worried, Slicehost will give you instances that will work like you're used to dedicated hosting working, but with many of the advantages of AWS.