It's about "the same" in my book. The accuracy of either is going to be based on the circuits driving it. That being said...while a magic eye might not have a scale/gradients you have on a meter...they respond to changes just as accurately.
Of all the magic eye tubes, my favourite is the 6AL7GT. It has two square sections at the top one rectangular section at the bottom. The upper left side is grounded and the upper right is connected to the discriminator / ratio detector output. The bottom section is limiter self-bias (which may also be the AGC, if used). You tune so both upper segments are at the same height and this should also give the largest bottom segment. There are a lot of different types:
I've got an old RCA with the "cat eye" and an older Philco with the shadow meter - Both pretty interesting concepts, and they work. I dread the day I have to replace either.
I always liked the little blue indicator used as the tuning dial needle on the old Eico tuners. It would blow bright when tuned. It seemed to be pretty sensitive as well. I've had a few Marantz tuners with O-scopes. Those are cool too.