The RTX2070 has an extra 2GB of VRAM and performs about 10% better in most workloads.
Most reviewers I've seen are actually able to match the performance of a 2070 by overclocking their 2060 and since both cards can ray-trace, the 2070 seems like a really poor value compared to its little brother, so the only reason you would want to buy a 2070 would be for futureproofing.
Your CPU will run fine with either of the cards, as long as the other parts in your build are OK.
For 1080p-1440p, I'd go with the RTX2060 as it delivers consistent performance at a reasonable price (compared to the rest of the lineup).
If you desire to game at a higher resolution than that, I believe that the RTX2070 is the best choice provided it is in your budget range.
The 2060 is fully a 1070Ti equivalent in performance in all the reviews I've seen; if you have a 4k monitor, or 1440P, get the 2070 for it's longevity in newer titles. (Although not quite the value to performance scale the 1060 was at $250, the 2060 is quite the value compared to the 2070 and 2080, and, although it is regrettable that $350 is the new 'midrange', it will remain so unless AMD's new forthcoming offerings force prices downward)
The question is in what resolution you planning the next few years. If you plan only to play in 1080p you are absolutely fine with the RTX 2060. If you plan to play 1440p you would be fine right now and probably for the next year. But if you want to be future proof in 1440p you might want to pick up the RTX 2070 because of the extra to Gigabytes of VRAM.
I play all current games in 1440p on my system and no current title is really using more than 6GB (well Far Cry 5 does, but only because its available, it would run the same way with 6GB since it only needs around 5.5Gigs for 1440p)
I'm definitely leaning torwards the 2060. One last question: if I'm trying to keep the build futureproofed for a couple years, do you think the 2060 can do the job?
For 1080p, most games I've seen won't exceed 4GB or VRAM, so you should be fine for years to come.
1440p is where things get a bit tight. The RTX2060 manages to deliver a smooth experience in the vast majority of the titles.
However, a handful of (mostly badly optimised) games can go over the 6GB limit and VRAM usage isn't going to drop in the foreseeable future.
I would still recommend the rtx2060 though, as it is an RTX2070 under the hood, with less VRAM at a significantly lower price.
For 4K, definitely go for the RTX2070, you might as well want to step up to an RTX2080 for futureproofing.
All in all, it depends on the resolution you plan to run at and the money you are willing to invest.
If money is the issue, you can wait for the AMD lineup, but but all we can do is speculate about its performance.