Both. It's a sliding scale. The scale goes like this:

- Completely summed before it reaches the speakers (0 separation).
- Speakers are super close to each other, such as being in the same enclosure (essentially summed unless the speakers are doing tricks with aiming and phase processing to try to mitigate the problem).
- Speakers are pretty close to each other but not exactly coincident, like in a boom box.
- Speakers are separated by approximately the correct intended angle, where you and the speakers form a right triangle (90 degree separation). This is the middle ground that mastering engineers are aiming for.
- You are directly between the speakers (180 degree separation but with some bleed over).
- Headphones (infinity separation with no bleed over).

Additive and subtractive phase interactions in the sound waves cause changes as you move up the sliding scale of separation. Instruments and voices recorded and mixed in stereo, depending on exactly how they're recorded and mixed (I can talk your ear off about mid-side micing and mono compatibility), will seem to decrease in volume as they become closer and closer to mono-summed. Instruments and voices recorded and mixed in mono and then placed into a stereo mix panned center (usually but not always lead vocals, bass, snare drum, kick drum) will seem to increase in volume as they become closer and closer to mono summed. The amount of perceived change can be as much as 6 decibels or more in either direction, as you get closer to the extreme ends of the scale.

The frequency spectrum of the particular instruments and voices is also a factor, since the amount of separation and the listening position will affect which frequency nodes are the ones most heavily affected. This is before we even get into the question of having the woofer summed but the tweeters not summed, which muddies the mess even further. So now you're not only talking about the balance of instruments changing, but now the issue starts to change the EQ response of each of those instruments too.

Music producers and mastering engineers try to fix this as much as they can with little tricks and compromises, but they can't fix it completely. God knows I've tried. The only true solution would be to mix entirely in mono, but then the music would sound flat and lifeless like an AM radio. Some of it can be mitigated by fiddling with the EQ settings on your stereo system, but that's not a perfect solution either, since you're trying to change the perception of lost or increased information without actually changing the source of that information.

The kind of ceiling speakers you describe, with the stereo inputs and dual tweeters, are intended for restaurants and such, or for people who don't care about the music itself, where it's meant as just background music and not for quality listening. You'll get variable results depending on the amount of electronic and physical trickery they're doing to try to make the speakers sound good. Sometimes speakers like that can actually sound quite good if they're a really good brand and everything is set up properly, but they'll always be a compromise of all the factors I cited above. Some people even like the way the music sounds after it's gone through that play dough fun factory, since it tends to increase the perceived volume of lead vocals panned center.

If you're getting high quality ceiling speakers with dual aimed tweeters, then at least try to set them up in the correct positions relative to each other, so that what little stereo projection they have are all aligned. If you install them in "69" positions relative to each other, then you'll have nodes where you're getting all right channel or all left channel from multiple sets of tweeters depending on where you stand.