People always ask me "Why rubidium?" and it was fun to finally get to look into the answer. We use ${}^{87}$Rb in my lab.
And I think it's worth first asking the question in exactly that form: why rubidium?
I think the answer is largely historical.
Rubidium actually got laser cooled a little later than some other common atoms, but then it was realized that CD drives had diodes that worked at 780 nm, the wavelength needed for laser cooling Rb. This brought laser cooling into the reach of a lot of labs that didn't necessarily have huge amounts of funding for the early laser systems.
There are a couple of other good reasons for rubidium to have been historically chosen, as well. You have to understand that the holy grail of early atomic physics was getting a BEC, a Bose-Einstein condensate. And all thoughts were geared in that direction. So when they found an atom with a positive background scattering length, whose atomic cross sections also made evaporative cooling meaningfully useful, they believed they found "God's atom" (this quote might come from Eric Cornell).
***Edited to add: "historical reasons" might not seem like the best justification (which it isn't), but remember that, even now, a good number of PIs and faculty in atomic physics were grad students, postdocs, and early-career faculty when laser cooling was still new, so these historical reasons came at a time that shaped their thinking for the rest of their careers, and therefore the design of their experiments, the ones producing papers today. My PI still talks about the old dye laser systems sometimes.
As a note, ${}^{85}$Rb actually has a negative background scattering length, which makes BECs unstable unless you use a Feshbach resonance at a fairly large magnetic field to make it positive. This puts it at a historical disadvantage.
But there's actually a better reason not to use 85 in your specific application, atomic clocks. It's simple and already stated here on the thread: its ground-state hyperfine frequency of 3-ish GHz is smaller than 87's splitting of 6.8 GHz.
This is why cesium, at over 9 GHz, is still the world's standard, and why the new strontium optical lattice clocks (which work at 429 THz) are the world-record holders.
When you think about atomic clocks, the absolute first question you have to ask is "How fast can it go?" The questions of quality and stability are engineering questions; the fundamental oscillation frequency is something you can never get around except by changing the basic setup.
You want to be reaching for stability that matches the fastest oscillation you can get, not settling for a slower clock that you can get really stable.
The related statement I should make is a different way of thinking about the quality factor. This quantity is defined as $Q=\nu_0/\Delta\nu$. That is, for a given quality factor, a higher resonance frequency requires a higher linewidth. And since $Q$ is generally in the denominator of the instability, higher $Q$, means lower instability. This means higher resonance frequency gives lower instability... if you can keep the linewidth down.
Now, two isotopes of rubidium don't differ too much in the basic atomic properties. In particular the fundamental stability limit, the linewidth of the excited state, will always vary very little between isotopes. I can't seem to find a comparison of the atomic linewidths of the transitions actually used in rubidium clocks (the two-photon transitions or the actual "clock transition"), so as an example, the 5P to 5S transition, the linewidth is 6.066 MHz in ${}^{85}$Rb and 6.059 MHz in ${}^{87}$Rb. Getting down to that fundamental limit is just engineering, and any laser and vacuum systems that will work with 85 will work with 87 since they only really vary by being isotopes. (If anything, 87 I think is easier to trap due to lower vaporizing temperature, but don't quote me on that.) So the linewidth can in fact be kept about constant between the two isotopes.
So if you're going for rubidium, you want the faster oscillator with the same linewidth: ${}^{87}$Rb is the way to go.
