I've got a Debian Wheezy VM on Linode and they run it with their own kernel.
As a reputable company, I'm sure they're quick to apply security patches, and all I need to do is reboot to get the new one. However, to notice whether a new one has been released, I have to monitor an RSS feed, which will require a fair bit of looking at as it includes notifications about all kernel releases, not just the one I'm using. Also, using their kernel which is outside of my OS causes pages of warnings about assumptions from things like my firewall script which is trying to check for the existence of certain modules.
I'm already on the Debian Security Announcements email list, which I keep an eye on for my other VMs.
So it seems to me I'd be better switching to a stock Debian kernel, but are there any other advantages to using a host's kernel that I might not be aware of?