You can share
/usr/local. Sometimes the two distributions will have different versions of libraries available, so you may need to install a few libraries on one side or the other or in
/usr/local itself. The burden of installing the odd extra library is likely to be compensated by not having to maintain two installations of each program in
If there are programs that you only want on
/usr/local for one of the systems, you can make a different arrangement: don't share
/usr/local, but share a stow repository, and make symlinks into the
/usr/local of both systems.
You don't need to put
/usr/local on a separate partition to share it. You can store it on one system's system partition, mount it wherever you want on the other system, and create a symbolic link.
You cannot share
/var. There are minor differences in how the directories are arranged, and each distribution has its own user IDs. You may be able to share parts of
/var, for example the mail spool.
/var is huge. You don't need that for a basic system. If you're going to put a lot of data there (e.g. because that's where your web server root is), size the filesystem according to your data. There's no point in splitting
/var from the root partition, so combine them. You don't mention
/usr in your list: this too needn't be split from the root partition. Just make one system partition for each OS, plus a shared
/home. You do need more than 15GB for the system partition, unless you're going to be very conservative in the programs you'll install. Make a 50GB system partition and you'll be fine.
There's no need for a separate
/boot partition unless you have additional requirements such as encrypting the system partition.