The reason I moved to AWS was because when I added a new (cheap) hard drive to my dedi, they didn't put a partition table on the disk. When the machine rebooted, the superblock got overwritten and I lost access to the file system. (I did manage to recreate the superblock and get the data out, but jeese...)
One time I made a ticket and somehow my record in the trouble ticket system got screwed up and I couldn't put more tickets in. Some wizard fixed that in the SQL monitor after I talked to 3 other people who had no idea this could happen.
As for costs it's not so simple. I've got a processing job I run each week that costs $6 of CPU time because I pay just for what I need. I wouldnt want to run it on a dedi because it's a beast.