Haven't seen a Hornady, but on the RCBS press mounted swager.....lots of leverage meant barely noticeable slip in, the stop, then very noticeable pull to get the darn button out of the primer pocket....hated that part.
Haven't used a Dillon, but the RCBS bench swager is similar and is nearly no effort at all......
but it has no casefeeder!....and no swager has any guarantee that the metal didn't spring back some to make seating a primer a PIA. So with the RCBS Bench swager when I used the Trim Mate to to uniform pocket depth.....IF it didn't just slide in the uniformer, I had the military reamer just behind to ream it just a tad so I could then uniform it and thus guarantee my progressive wouldn't have a hickup. ;)
Video of that (much slower) operation below: (steps illustrated: swage, then uniform pocket depth for my progressive, then deburr the flash hole.)
Https://vimeo.com/385807496
BTW the one that didn't work in the video still had a spent primer in it :roll:......took me long enough to look....doh........