I was working on this project literally last month June 20th with AE 2014, and no I can't open the same file in 2015. So why was my RAM enough to work on this project but now is not?
I obviously will be trying to reload AE 2014, but this seems to be so jarringly different that I must be missing a setting, I can't imagine that it wasn't tested to get benchmarks for comparative memory allocation between the two versions of AE. 2014 vs 2015.
In order for anyone to give you an actual answer to your question, they would need to know a lot more information. Primarily things like the content of your compositions. I've not had any major problems like that opening projects in CC 2015, so something must be different about your setup.
By the way, it's pretty easy to re-install CC 2014 (or CC or CS6, for that matter): How to Find and Install Previous Version of Adobe Apps in CC 2015
In the future, I would recommend keeping your old software versions when a new one comes out. Here's how: Creative Cloud Delivering More Choice for Installations