You can install Synaptic Package Manager on KDE, but there I would use
KPackageKit instead of Synaptic Package Manager.

One thing you can do, however, is to compare the /etc/apt/sources.list file for
both the 32-bit Ubuntu 10.04 and the 64-bit Kubuntu 10.04. I imagine then
should be different or in some way be able to resolve the 32-bit vs 64-bit
differences.

That being said, for Synaptic Package Manager, you need click on reload to get
anything new since last time. There is a slightly different equivalent for
KPackageKit in KDE environment.

For Ubuntu, you should try installing the KSplice upstart manager in order to
install kernel security updates without rebooting. I do not know if it also
applies to Kubuntu.

One thing the KPackageKit does that Synaptic does not do is to differentiate
security updates into a separate category, and you can install them all, but I
am not sure about doing it ala carte instead to give you a choice.

As you say, you are getting by with apt-get update, but one thing to make sure
is that you have repaired any errors you may get, like if there are keys you
need for separate repositories to install specific packages, etc.