Gauging how much a game was improved when you’re not seeing a direct comparison against old footage is always difficult. There is an element of rose-tinted glasses at play, and memories of older games we loved are always a bit charitable. Which is why we often see comments mentioning that the difference is not visible, when it totally is.
The Elder Scrolls V: Skyrim Special Edition is almost out, bringing completely overhauled graphics to fit the new generation of consoles, and a fresh coat of paint (free, if you have all the DLC) on PC as well.
Today the good folks at PlayStation Access published a very well made comparison video that shows exactly that, and demonstrates that things have changed quite radically on the PlayStation front.
Of course, on whether the game in itself has aged well or not, your mileage may vary. You could also say that your modded original Skyrim on PC probably already looks better than the Special Edition, but if you like to play vanilla or on consoles, the improvement is certainly massive.