I have a Intel 2500K at the moment
Would I see much improvement in turn time for Galciv3 with a Ryzen 1600X or equivalent?
Ryzen definetely better in single-threaded performance than 2500K/2700K/3570K/3770K when compared with equal frequency. And 1600X got two more cores and SMT (there are 12 threads), so multi-threaded performance much better.
I think GalCiv3 will benefit from this upgrade.
How does Ryzen vs Intel in same price range match against each other?
Current i5-7600K got much higher frequency, and slightly better performance per core when compared with equal frequency, but still cannot compete in multi-threaded tasks.
Also there are new CoffeLake generation, i5-8600K, i5-8400. These i5 CPUs got two more cores (than i5-7600K) but still miss SMT. So only 6 threads, but may be for many people it will be enough.
On the other hand, there are i7-6800K and i7-7800X, they are comparable with 1600X in most of the tasks and games, but have a much higher price (because of PCI-E lanes, RAM channels, etc.) and requiring expensive motherboards.