The differences in screen resolution depend a bit on what you're looking at.
If you regularly read things written in a logographic character set or something with a lot of detail (Chinese, Japanese, Korean, Arabic, etc.), it is night and day. This can also include Western languages with lots of diacriticals (accents, umlauts, macrons, etc.) as well as other notational systems (e.g., mathematical symbols, music scores).
If you have a Retina iPad (mini or regular size), and a non-Retina version side by side, go visit
www.apple.com/jp/support (Japanese language Apple support site) and see for yourself. You don't even need to read Japanese to see the visual difference.
I noticed myself at the Apple Store that if you are looking at a full-page printed PDF (8.5x11") on the original iPad mini, I frequently had to zoom into read things. That's why I didn't buy it.
Here's another example, a PDF score of Beethoven's Ninth Symphony:
http://www.musedata.org/beethoven/sym-9/ (web page)
or this PDF score of Bach's Goldberg Variations:
http://imslp.org/wiki/Special:ImagefromIndex/229423 (PDF file)
This is not the case with the Retina mini. One can read full-page PDFs on this device without zooming.
Some -- not all -- games take advantage of the better graphics of the Retina version.
And yes, photos and videos look way better on the Retina model.
In the end, it's up to you. After my iPhone 4S, iPhone 5S, and now my Retina iPad mini, my next computer screen purchase will be Retina-caliber monitor.
Note: my Retina mini replaced an iPad 2 (non-Retina display); I waved goodbye to that device (Amazon is buying it back).