make-kpkg is a command from the package
kernel-package, which used to be part of the official packaging infrastructure for the kernel packages that get shipped in the Debian distribution. It is not being used for that purpose anymore because the current maintainer for the kernel packages inside the Debian distribution chose to stop using it; however, the authors of the
kernel-package package have not stopped maintaining it, so it is still an officially supported way of creating your own Debian packaged version of a kernel. It has various options and targets; the most important ones are the ones you refer to in your question, i.e.,
kernel-image (which builds a package containing the kernel and modules that you selected during
make config), and
kernel-headers (which contains the include files that you might need if you want to compile an out-of-tree module). The
kernel-package package is maintained as part of the Debian (or derivative, like Ubuntu) release with which it was released, so as a result if things change in the Debian infrastructure then newer versions of
kernel-package will be updated to incorporate it, and they will ship with that version of Debian. As a result, a kernel package created by the
kernel-package package is always tailored best for the version of Debian on which it was created. However, if things change within the Linux kernel in a way that makes
kernel-package break, then updating your kernel package for a stable version of Debian may be somewhat complicated.
make deb-pkg is a target in the Linux kernel's build infrastructure. It receives patches from Debian developers, but as it is not maintained within Debian itself, it always uses the tools and policies that are most up to date at the point in time where the kernel version you're trying to build was created. This means that in some cases, it might try to use a tool that isn't available on an older distribution yet. As it is not maintained inside Debian, it is not an officially-supported method (at least not from the point of view of Debian) for creating kernel packages; having said that though, it is mostly maintained by people who are involved in Debian, and so there is no reason to suspect that it won't work.
Whichever method you choose is just a matter of preference; unless you are heavily invested in peculiar outcomes of the package building options, both methods will work just fine.