The physical design (Grand vs Upright) has a profound result on the expressive nuances experienced by the pianist while interacting with each respective mechanism. However, if we keep it simple, the fundamental differences can be described as primarily a difference in feel and a difference in sound.
The following video by Steinert Tech Jonathan Kotulski helps explain the major differences:
A Difference in Feel
In a grand piano, the hammer rests horizontally and moves up towards the horizontal string, and then is returned to its starting position by gravity. The keys are weighted by hand in the factory to counteract this force of gravity. This creates an even feel across the keyboard, and just a bit heavier feeling than an upright. When playing, the musician feels a powerful connection to the sound through this even weighting of keys and hammers. The pianist can deliver their full expressive capabilities, rapid repetitions and trills, at whisper soft and thunderously loud dynamic levels. On a grand, every time a hammer hits the string, it then resets quickly, perfectly, and predictably for the artist. There are many other fine details in a grand piano mechanism that make it the absolute ideal, the very best example of what a piano should feel like.
In an upright piano, the hammer stands up vertically and moves towards a vertical string, and then a little spring moves it back to its resting place. Gravity is not part of the equation. The keys are weighted in the factory to counteract the force of each individual hammer return spring. The upright action mechanism works very well, but the design is trying to simulate the experience of a grand. The upright action design approaches the perfect grand design but always falls short. It is effective and functional, and the key weight still feels consistent, but on an upright piano overall the pianist will experience a little lighter feeling and slightly less responsiveness when playing with fast repetition and trying to control dynamics.
A Difference in Sound
In a grand piano, the sound is projected by the horizontal orientation of the soundboard and strings, mostly projected up and out. The strings vibrate, the soundboard amplifies this vibration and the soundwaves are sent up and out - they hit the lid and are directed throughout the room in every direction. The artist sits and plays in the middle of all this sonic activity, fully immersed in the sound. Typically, a grand piano has longer bass strings than an upright creating a deeper and richer content of frequency in the low range. This combination of frequency spectrum and spatial activity of the sound make it the best experience of a piano, and allows the artist and audience to enter inside an amazing listening experience: hearing the full frequency spectrum and feeling the powerful vibrations. It could be compared to a surround sound speaker system.
In an upright piano, the sound is dispersed by a vertical soundboard, mostly projected away from the pianist towards the wall. Additionally, some sound is projected towards the pianist as well. The sound is not as free to move around the room in an upright as it is in grand, but still gives the artist an immersive and intimate experience of the piano tone. This could be compared to a mono or simple stereo speaker system.
And the winner is:
Ultimately, the upright piano is an approximation of the grand piano. The design of the grand piano is the highest standard of excellence, chosen by artists on concert stages everywhere. Yet, with uprights - the economy and space-saving aspects are often the rational choice. Whatever piano you choose, take time to learn the difference and experience both types of pianos!