Even though that DSLR is eight years old, it gets battery life that any mirrorless camera can only dream of
I swear that my 2008 Nikon D700 had functionally unlimited battery life. My mirrorless camera would be hard-pressed to get through a day of shooting on vacation on one battery, but that tank seemingly had a Mr. Fusion inside of it.
They are very different. Even though that DSLR is eight years old, it gets battery life that any mirrorless camera can only dream of (>1000 shots without a battery grip). Even though the mirrorless has one of the better EVFs among it's peers, the resolution is not quite as good as the OVF, and it does have visible lag and smear that the OVF simply doesn't have (the EVF is a 85 Hz OLED with 1280x1024 pixels or something like that, iirc).
The DSLR has a faster AF if you are wildly out of focus, though the AF is overall much worse - the mirrorless has like 10x as many AF points, and they are all over the frame, and it has flawless video autofocus, as well as almost perfectly accurate autofocus.
The full-frame mirrorless is about the same size and weight as the APS-C DSLR. A full-frame DSLR would be quite a bit bigger and heavier.
The real difference is that you get a lot of stuff just like that in a mirrorless which are somewhat of a pain in a DSLR. Viewfinder magnification, good video AF, silent shooting with the viewfinder, customizable finder display, nightvision, histograms, distortion correction in the finder (critical for precise framing with ultra-wide lenses), focus peaking etc.
There are some differences which are pretty much purely hype. Things like eye AF for example pretty much only matter for people who mostly do "ultra-blurry background" portraits which have such a thin depth of field that when the iris of the eye is in focus, the eyelashes are already blurry. It's a very specific thing to do, but gets around 90 % of the air-time in "totally independent reviews I swear I'm not sponsored".
At the current top-end, DSLRs like the Nikon D6 are said (not that I would have any idea about that) to still have somewhat faster AF than comparably expensive mirrorless cameras.
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As for Sony, they inherited the A-mount when they bought Konica-Minolta. The A-mount was at that point in time already a legacy mostly-mechanical-with-some-electrical-bits-kind of mount (e.g. mechanical aperture control, mechanical autofocus through a coupling in the mount). The E-mount is a modern, fully electronic mount, though designed for APS-C (full-frame just barely fits into it). I think when the E-mount was introduced it should have been clear that anything A-mount is on the way out. Also, A-mount SLRs where never particularly high-end, so in terms of performance I'd expect them to be significantly below what Nikon and Canon offer, especially because it does not seem like there was much development on these after the E-mount was introduced.
Just like Nikon F is clearly on the way out with Nikon Z being around, an Canon EF being on the way out with Canon RF around, the same is true for the A-mount.