I do not speak as a professional designer, but:
There are 30-day free trials available for both, so you could try them for your tasks and see whether one is sufficient. The fixed dark-grey/light-grey UI of Elements you may find annoying.
Many of the extras that full Photoshop provides are for sophisticated photo retouching and print-ready editing (CMYK support). If you are exchanging files with other designers nothing but full Photoshop may suffice (though other programs can read and write PSD files). If you want to use certain plugins that may also be true. (Adobe keeps crippling the kinds of plugins Elements can use. I am not sure what the latest situation is.)
You may find free programs such as paint.net (http://getpaint.net) or The GIMP quite sufficient for your needs now.