Yes, though less about interference and more about signal strength. The greater the divide in signal strength, the more likely it is that devices will roam.
So by using higher gain antennas, you increase the signal strength on the current floor, while reducing it on the floor below.
This of course reduces interference, but ideally you are setting seperate, non-overlapping channels on each access point already, so there would be no interference even if they were sitting practically on top of each other.
Omni-directional antennas produce a donut pattern. The only ones that is "perfectly spherical" is an isometric antenna, which as no gain (an antenna's gain figures, dBi, are Decibles of gain standardized to a perfect isometric antenna, hence the lower case i after the dB).
Basically any antenna is compressing the radiation pattern to increase the signal sent and received. Whether it is a panel, yagi, parabolic, omnidirection, etc.
In the case of a general omnidirectional antenna, they are generally a dipole type antenna, which produces a normallize 2.3dBi gain for a halfwave dipole antenna, which basically is going to look like super thick donut. The higher the gain, the flatter the donut looks.
That is what it looks like visualized. What you get in number form is something called the HPBW, or half power beam width. This is how far off the centerline of the antenna radiation power you can move before the signal drops to half the maximum (half being a 3dB reduction in signal). In general, the further from this HPBW "spot" the faster it'll drop off as it generally isn't a very gradual thing.
So something like a 2dBi omnidirectional antenna might produce a HPBW of something like 75 degrees, which means if you are 37.5 degrees above or below the centerline, you have hit half power (or 3dB lower). If you moved to 45 degrees off the centerline, you might be down to quarter or less power (or 6-8dB loss).
A 5dBi antenna has a HPBW of around 32 degrees, which means more than 16 degrees above or below and you are at half power. At 30 degrees above or below, you might be easily down to a quarter or less. Of course, the interesting thing here is, because the gain is higher to begin with, at 16 degrees above or below, you are actually at a signal strength equal to "sweet spot" of a 2dBi antenna, because the loss at 16 degrees off centerline is 3dB, bring the 5dBi effective gain down to 2dBi effective gain. Of course it losses signal strength faster, as I mentioned, at 30 degrees, you might be facing a 6-8dB loss, making is 1-3dB negative when taking in to account the 5dBi antenna gain. With the 2dBi antennas you might only be a 0dB net gain/loss 30 degrees off (because you aren't quite out to the HPBW).
An 8dBi omni has roughly a 15 degree HPBW and it gets better or worse the higher gain you get.
Hopefully that helps illustrate a little on how they are working and why a moderately high gain antenna, like a 5-7dBi antenna can really compact things by reducing the signal below the access point, while also increasing it on the same floor.
As a further example, if you were on the same floor with the AP sitting at desk level, say 3ft off the floor and you were holding a tablet in your hand at 4ft high, that is easily within the sweet spot of any reasonable wifi antenna if you were on the same floor.
However, a floor below, unless you are really far away, holding that same tablet 4ft off the floor, the AP is roughly 8-10ft (figuring typical 8-10ft ceilings, plus joist and floor thickness) above you. So to be in the sweet spot of a 5dBi antenna in this case (16 degrees below or better), you'd need to be standing around 30 feet away from the access point on the floor below, which is going to put a lot of walls and floor between you and the AP, and the signal is going to be going through the floor/ceiling at a very oblique angle, further killing it, where as the AP on the same floor you are on, is in the sweet spot for its antennas and they are higher gain now too.
Using 7dBi antennas (about 20 degree HPBW), you'd have to be 46ft away to be "in the sweet spot". That is only using the 8ft figure, if you have 10ft ceilings, its more like 38/58ft respectively.
Win win.
