Owned an R390A (EAC) and it was rebuilt according to Chuck Rippels notes, caps replaced including the recommended "death caps", It was fully aligned (stagger tuned) and even polished to a high luster shine in my shack.
Perhaps I am going to come across as being verbose, but you asked a question, so I am going to attempt to provide as much detail as possible as I feel this will give you a well rounded answer to your question.
So here, I have done direct comparisons using the R390A with other receivers in my shack. This consisted of switching a coax switch, using the same antenna, with rigs all tuned on the same exact frequency, while flopping the switch on the fly, back and forth between various rigs and receivers in my shack until I practically wore out the coax switch.
It's also important to know that I also constructed an audio switch box I made which enabled me to switch all the receivers in the shack to use the same speaker setup in the shack. I wont go into too much detail about it's design, but it was a somewhat elaborate speaker setup (not car audio / stereo speakers) and it consisted of some large paper cone speakers, installed in large wooden enclosures that could easily discriminate the differences and for the most part and the speakers I used sounded great. I feel if you are going to compare something like this, you should probably ensure you are subjecting the equipment to the same antenna, frequency and speaker during your testing which I felt I was doing.
I compared the R390A to some other SW receivers. It basically blew away the Hammarlund in both sensitivity and sound quality. Same thing with a BC-348Q. But then, a BC 348Q is as wide as a barn door so that isn't really any surprise. The other SW receivers in the shack, both solid state and the heavy metal variety, are not even worthy of comparison, as the R390A was the clear winner in the consumer SW receiver comparison category.
Another receiver it was compared against was a General Dynamics R1051B. This is basically the military radio that eventually replaced the R390A as far as the Navy is concerned anyways. I found the R1051B sounded a little less "wide" on the receiver filter end of things. As far as sensitivity goes they were about the same really. As far as looks go, The R390A looks much more impressive and is actually easier to tune around on the bands than the idea of using all the selective dials to change frequency on the R1051B though. Guess you actually have to change frequencies on an R1051B to understand.
Well enough playing around lets get serious.... I fired up the FT1000mp MkV and the R390A and tuned into a weak station on the Mark V. The R390A struggled on SSB when the signal was fading in and out of the noise floor compared to the Mark V. The Yaesu could discriminate the signal much clearer in weak signal noise floor conditions. It's not that the signal level was actually any better or that much worse on the R390A, it's just that the audio portion of the weak signal didn't sound as "sharp" or "modernly processed" as the Mark V demonstrated. It seemed like the R390A "knew" a signal existed, it just didn't know what to do with it to make it sound intelligible?
However, the R390A seemed quieter on receive on AM. There was less static at the noise floor. I also found "most" typical signals ranging from S3-S9 had a more robust and full sound on the R390A. The rice box, well.. sounded like a ricebox..lol
Just for kicks, I also compared it to a Yaesu FT 817 and FT 847. The R390A can't fight adjacent signals as well as the MarkV does, but it holds up in this respect to the FT 817 pretty good. In fact, the R390A could actually hear better than the FT 817 did, especially when using the mechanical filters on the R390A. Keep in mind, the FT-817 I used had no filters, and it isn't known for it's superior receiver specs. anyways though.
Similar to the Mark V, the FT 847 actually pulled in signals better than the R390A did when signals were at the bottom of the s-meter, but there's something about the R390A audio that sounds better on normal signals. It has a richer tonal audio quality, but when the signals dipped down into the mud, both the FT847 and the Mark V could pull them out better although, it wasn't by a large margin. It seemed like anything less than 1 s-unit and below on the R390A wasn't going to be heard clear enough to receive. It's just the garbled existence of a voice heard mixed in with noise floor static on the R390A.
However, the fidelity of AM shortwave signals seems to sound better on the R390A than the rice box rigs did. It has nothing to do with the receiver "specs. /sensitivity" or anything like that though. I think it had more to do with the actual "listening experience" than anything else.
I think people are trying to suggest the R390A is often just as good as many modern day receivers in terms of "specs". I would have to conclude the R390A is very good and even better when compared to many other SW receivers of a similar era, but there is no way it's as good as a typical contest rig is today. So no, they really don't outperform modern rigs in reality as far as "specs" are concerned, however, if you ever used one, you would clearly understand that's really not the point of using an R390A anyways.
They DO however certainly outperform a modern rig in term of beauty and craftsmanship, when compared to a hunk of manufactured molded plastic sitting on a desk though.
I think this is where the vintage car comparisons come into play. Vintage cars don't come equipped with XM radio, Onstar or even get good gas mileage for that matter. So comparing features, specifications and performance really isn't the point of owning a vintage car any differently.
Hope that helps.