But before you got 4 tries with 4 keys. Has anyone done the math to see the percentages with 4 relics and one mission versus 4 keys and 4 missions?
This is pretty close.
tl;dr if you're farming for one particular rare part, and everyone is using Radiant versions, you have a 34.4% chance of getting the item on a particular run. Compared to the 2% chance you had with a single key, it's a stupidly big improvement on the chance of getting that rare part. In fact just playing with one radiant relic itself (2% -> 10%) is a 400% overall drop chance improvement AND you're reducing the chances of a common drop. Plus, on most missions, your time to complete is way, way shorter than anything that the Void ever had other than exterminate.
The interesting part is that while this sounds like a good thing, in practice you still need ~11 runs, which means 11 relics at Radiant level. So the chances are certainly much better in the new system, you'll have to farm those 11 relics and the traces if you want to buff up your drop chances.
Now it's not exactly hard to farm traces, you get them just doing the relic runs normally. Even the lowest level still nets you 10-20 traces without a relic. It's just going to be more difficult to farm out the parts sequentially, doing the same thing over and over.