Intel will never go toe-to-toe with AMD on pricing, at least not in the long term (1+ years), and unless it's approaching bankruptcy, which I assume isn't the case for now.
Intel's chips are the best value for the money right now because AMD totally messed up its last microarchitecture. They bet on something (high parallelization) that didn't pan out. And they suffered greatly for it. Kind of how Sony went with the Cell processor in the PS3 (although Sony did make the best of it in the end).
But Zen completely changes that equation. Zen is basically a direct and very close competitor to Intel's current microarchitecture and they should have rather similar performance.
However, It doesn't mean AMD's chips will necessarily beat Intel's chips in "peak performance". Because for one, Intel still has a better process technology, and second, AMD still had to compete with a moving target (albeit a very slowly moving target - Skylake is only like 20-25% faster in single-thread performance compared to Sandy Bridge).
But I imagine Zen is going to be within 10% or so of Intel's equivalent chips in single-thread performance, but potentially much better at multi-threaded performance if AMD actually sells twice as many Zen cores in its similar priced chips (8-core Zen vs quad-core Core i6, quad-core Zen vs dual-core Core i5, etc). On top of having more cores, AMD may also offer lower pricing points that outweighs the 10% difference in single-thread performance, but that remains to be seen (I probably wouldn't do that if I were them, as double the cores at a similar pricing point should be more than enough value for money).