As far as features go, you'll still get all of the root access features you would with a dedicated server. Just make sure your VPS will have enough CPU and RAM to handle all of your sites. You could take a look at HudsonValleyHost, I used them to host a large number of small websites and a few larger ones. They're quite affordable and comes fully managed.
@FelipeK, just be sure to examine your current resource usage (CPU, Memory, Disk IO, Network, etc.) before making the move. If your server has a lot of power to spare, a downgrade probably won't hurt much. With a quality provider there's a good chance that CPU (burst) and disk performance will improve (depending on your server configuration). Sustained CPU performance could drop (again depending on your current server configuration).
I think you can go ahead with a vps rather than a dedicated server but make sure that the resources available to you is sufficient enough. There are many hosts available out here to suit your needs, just have a look over them.
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I think you will be better off staying with the dedicated server you are on right now. Is there any specific reason why you are downgrading?
You will see a difference from going dedicated to a VPS server.
Just analyse your current sum requirement of memory utilization on your dedicated server and compare with VPS . If all is set as per requirement. I would recommend to move. But still take a image backup of your dedicated server before doing an migration.
I agree with Hostnesta and Mike. You say you have 15000 uniques a day on the largest of 70 websites. That does not sound like something a cheap VOPS plan could handle and if you go for a high-end VPS, chances are you will only be saving pennies compared to a dedicated server.
First of all, like some other posts above. A low-end VPS will not be a good solution to your needs. And since you are not a host guru or anything. I would suggest that you buy a high-end managed VPS as it will be cheaper than a managed dedicated server. But if you aren't constraint on your budget then I suggest getting a managed dedi.