Q: How to extract data from old hard drive in enclosure to new Macbook (El Capitan)

I know this topic is discussed pretty extensively, but I've been having issue finding the correct instructions that relate to my scenario.

Recently my Macbook pro, late 2011 running (10.9.5) sustained water damage to the logic board. I have since replaced it with a new Macbook Pro Retina (10.11.5).
I would like to move pretty much everything over to my new Mac. This includes software, music and edited photos on Adobe. The old hard drive seems undamaged and runs from a powered enclosure.  I can view most of my data in finder but it wont show up when running migration assistant and it appears on startup disk, but wont let me click on the the external hard drive to start it in target disk mode (Is this because it is not updated to the current software?)

Can someone please direct me to a suitable guide for transferring my old data or updating the old hard drive to el capitan (if that is the problem).

Thanks in advance.