Grand pianos sound much better because they are better. :-)
Just kidding. Grand pianos are constructed a bit differently as has been noted, but the biggest thing is the sound is project up and out from the instrument and not towards the user with a lot of wood in one's face. An upright piano also has its action in front of the strings unlike a grand with the action underneath and striking the strings from behind. This also affects the sound, making an upright sound much different.
On an upright piano, the pedals work differently. The upright's una chorda pedal works by placing the hammers closer to the strings to make the piano play softer. This is a totally different mechanism where the hammers are moved over and strike two strings, rarely one string, on a grand piano. The tres chorda pedal on both works in a similar fashion with the string dampers are lifted off the strings to allow the strings to vibrate. The sostenuto pedal is a rare beast on an upright. They do exist but only on the really expensive ones. Many uprights that do have a middle pedal, are fitted with a practice pedal which puts a thin sheet of felt between the hammers and the strings. This creates a muted sound so the piano isn't as loud and intrusive, and allows for much later evening practice.
Overstringing does not increase the length of the strings. What does is create harmonics in the open part of the strings. Up until the mid-19thearly 20th century, even grand pianos were straight strung, with a mix of both straight strung and overstrung instruments around. Erard was still making straight strung concert grand pianos right up until the 1920s.
Here's a place that's worth visiting should you be able to. This is a collection of antique pianos that can be played on and heard. I have play on all these pianos listed on this website.
http://www.frederickcollection.org/collection.html
The main site is http://frederickcollection.org/