A VPS is shared infrastructure, so no real advantage over shared in respect of another user causing a blip.
You have 2 fundamental types of VPS, 1 has fixed resource, the other has a share of the host server. To get fast response times on a VPS you need to be buying similar resource levels to a dedicated server so will not really save much (if anything) over a dedicated box. On a shared node, you may well be able to burst to above the resource levels you pay for.
The advantage of a VPS is that you control the configuration, you can do anything (virtually) that you can do on a dedicated box.
The disadvantage of the VPS is that you have a server to manage, all this is taken care of on a shared host.
A good shared host will be as fast if not faster than an average VPS, a cheap VPS is likely to be on a host node that is just as overloaded as a cheap shared host so potentially you could end up with a slower site by moving to a VPS.
You need to look at the value of the sites and work out the relative costs for your particular use. You tend to get what you pay for in the hosting market, so tread with care.
I run both dedicated servers and VPS's, each has it's own merits and I select the platform based on customer requirement.