For the valley-mountain gravitational time dilation experiments that I've done I use 5071A cesium clocks. Even though 25+ years old, no commercial clock works better for this portable application. That is to say, rubidium clocks and older model cesium clocks are not quite good enough to detect these tiny relativistic effects with confidence.
Others here have mentioned prices. Surplus rubidium atomic clocks can be found for as low as $100 on eBay. Surplus cesium clocks range from $1k to $10k, depending on model and condition. Factory new 5071A are close to $100k so no one I knows is crazy enough to do that. If you are very patient and lucky on eBay you will find 5071A for as low at $2k to $5k once every couple of years.
Out of curiosity, do the output formats of the different models differ? With output format I mean the way that the (current) time is represented.
Not being familiar with atomic clocks, my hope and expectation is that the output is something different than a single large integer (compare unix timestamp). :)
Just take your time. Some of us look for months and even years before we find one worth the eBay risk.
There is one fact to consider. I have heard that the 5071A clock is still ITAR classified. It's not because of "atomic" or "cesium", but because the internal design is so advanced that the US decided it was essentially like a military weapon.
If in doubt look for vintage models like 5060, 5061, 5062, or 4050, 4060, 4065 instead of the still current model 5071.