No, we really don't have significant statistical evidence. Even for the rocket family. And there is no need to look for the reference you can't find since this is all verifiable from public data.
The ULA workhorse was the Atlas 5. Over its whole lifetime, both under Lockheed and ULA, it had 95 launches of which one was a partial failure (declared success). Wikipedia is good enough for that.
The SpaceX workhorse is the Falcon 9. https://www.spacex.com/launches/ puts it at 176 launches with 1 failure and 1 partial failure. This is not counting one that blew up on the pad with the satellite aboard.
The measured failure rate of the Atlas 5 is 0/95. Of Falcon 9 is 1/176. Note that 0/95 < 1/176.
The measured "not perfect success" rate of the Atlas 5 is 1/95. Of Falcon 9 is 2/176 = 1/88. Note that 1/95 < 1/88.
Also anyone with basic statistical knowledge will immediately see that the sample size is sufficiently low that we cannot draw any conclusion at 95% confidence.
Now what Falcon 9 does have the crown on is the longest string of uninterrupted successes of any rocket family. They are now at 148. (Not counting, of course, the one that blew up on the launch pad with the satellite on board.) But not enough to be statistically strong evidence that they are best. Also ULA has over 150 launches across their rocket platforms without any being declared a failure - which exceeds SpaceX's current winning streak.
That said, I agree with you about ULA's advantages, and I agree that SpaceX is the future. But I'm not going to lie about the math. And the math says that there isn't significant statistical evidence that SpaceX is better on safety.