The 4GB is faster, but the 16GB has the space. What is the best way to install while taking advantage of the strengths of both. I have it installed on the 4GB, but worthless because I can't install apps, or upgrade. Is there a way to put the apps drive on 16GB, but use 4GB for booting?
Yes, there is. You can even do that without setting up a new system.
Create an ext4 partition on your designated boot drive and copy the contents of your
/boot directory onto that partition. Then, update your
/etc/fstab to include the newly created partition and run
update-grub. The official Ubuntu help site has a more in-depth tutorial.
If you feel uncomfortable doing all that manually, there's the option of using BootRepair to do the heavy lifting for you.
You may be interested in my experiences in doing this:
Basically I have the OS on the 4GiB SSD but enough space to install applications and do updates etc.