Don't forget to add the price of a new motherboard to the ryzen cpu. And, yes even 2 or 3 generations ago Intel parts (all still 14nm/16nm fab) will game far better than AMD chips due to higher ipc and turbo boost frequencies. Shop around, the i7 8700 non k should be a lil over $300 US where the i5 8600K is around $240. Its the new 9th gen i9 parts that should be around $500 US. Like I said, comparison shop a bunch, $450 sounds very high for last generation parts.
Edit: just be sure that you are purchasing an 8th gen intel cpu to replace your 8th gen core i3. Intel messed with the chipset and the 9th gen cpu's will NOT work in 8th gen motherboards.