Yeah, the 3400G is based on Zen+ like the 2000 series, not Zen 2 like the 3600, so it's not really worth considering for anyone not utilizing the integrated graphics. On the CPU side of things, it's basically a 2600X, but with a third fewer cores, and considering that processor costs about the same, the 2600X would be the better option. Or there's the 2600 (non-X) for about $30 less, if you want to put that money toward a better tower cooler and overclock to get 2600X-like performance.
As for the original question, "2700 vs the 2600x", a better comparison you might make would be the 2700 vs the 2600 (non-X)", which is about a $50 difference. The 2700 boosts a bit higher than the 2600 at lightly threaded workloads, but at more moderately-threaded workloads those boost clocks drop significantly to below 2600 levels to keep the power use in check. By comparison, the 2600, 2600X, and 2700X tend to only lower their clock rates slightly as more cores are utilized. You can certainly overclock any of these processors to about the same level though.
As for coolers, both the 2600X and 2700 should include the Wraith Spire cooler, though the 2700's version of the cooler gets an RGB light ring. The 2600 comes with the shorter Wraith Stealth cooler, with a heat sink that's about half as tall, though again, for the price difference between it and the 2600X, you could get a 120mm tower cooler that would cool better than the Wraith Spire.