Upright pianos have a different sound from grand pianos, and in some situations, that sound is certainly desirable. I wouldn’t necessarily say there are limitations, but the micing techniques somewhat different. Aside from room mics, I’ve had pleasing results micing the back of the piano (on the back of the soundboard, a few feet up from the floor) as well as hanging two mics slightly inside the lid, or both. I’ve also seen some uprights miced in a fashion that necessitates the upper portion of the piano facing the player to be removed and the mics being hung in front of the strings just above the hammers. Different micing positions will lead to different sounding results.
Synthme nailed it overall; i'd just add a bit more regardling the sounds of the three (or four?) main choices.
You have the spinet "sound" - which is pretty cheesy overall, but always has its place. It turns up occasionally in pop songs, and has a quaint charm to it. You just wouldn't use it for solo classical work or most backing tracks in a professional setting.
The upright is much loved as well; from the honky-tonk/rinky-tink sound that many bar rooms and tack-hammered instruments have. Even a little out of tune, they have a certain sound that fits certain songs perferctly.
Also in most cases, these two types never have the proper string length for good, serious bass, so they just don't work as solo instruments. (The strings are thicker, but not long enough for the true harmonic overtone series. It's a trick to get around the laws of physics) This is partially why a spinet SOUNDS like a spinet; no matter how much in tune it is, it will never sound quite right harmonically, nothing like a grand.
Both the spinet and the upright (and "studio" pianos) have vertical harps, which plays a big part of the projected sound too. Arguably, they sound better against a wall, too, and the room sound has a lot to do with how well it resonates.
Then of course there's the grand piano case style. The harp & strings are horizontal, and the hammers hit the strings from below, instead of attacking from the side. Ditto for the whole damper system. It does indeed affect the sound. Then of course there's the lid that helps project the sound outward on a horizontal plane. Of course, this changes the entire way of mic'ing it for a recording.
With a good concert grand - 7 feet or more - the string length vs. pitch & overtone series is true, and the bass is wonderful, not cheesy. ("Baby Grand" pianos can be just as bad as spinets and uprights; they too have shorter, thicker strings below middle C, and the first thing to suffer is the bass.)
The first thing I listen for in a piano is that low end sound. If it's not true, then it changes the whole point of the recording and the usefulness of the instrument.
It all comes down to what you need the piano sound for; Solo concert classical music vs. rock vs. pop vs. novelty.