The files should open no problem in pse 12, but certain kinds of layers like adjustment layers (curves,b&w, color balance, channel mixer, exposure, vibrance and selective color) can't be edited in pse 12.
Other things like layer groups are not easily editable in pse 12.
Not to mention a host of other features that photoshop cs4 has that photoshop elements 12 doesn't.
You should probably download the 30 trial version of pse 12 and see if it will do for your kind of work.
Download a free trial or buy Adobe products | Adobe downloads
If you aren't familiar with the creative cloud, which is subscription only, you can get the latest version of photoshop cc 2014 and lightroom 5.6 for around $10 a month
(plus photoshop cs4 is out of the upgrade loop anyway)