In detail eh?
Some of you will get it...
The advantage of the levergun = fast cycling. Is that important? Only if you miss the first shot.
The advantage of a bolt gun over a levergun? Primarily the cartridges (and the diversity of cartridges) that they're chambered in. Talking modern manufacture leverguns, you're really looking at pistol cartridges like the .357mag, .44mag, or .45colt. Still a few .44-40's kicking around, or you're talking .30-30win, .45-70, 444marlin, or .450Marlin. At the end of the day, all of these rounds are big slugs, moving very slow. The .30-30 is a bit of an oddball for the group, but other than the Leverevolution rounds, still required a round nosed bullet or flat nosed bullet, and only pushes them to around 2200fps, way too slow by today's standards.
Sure, the 308Marlin is trying, but nobody has had confidence that it would stay the course, so it's been a slow start for them.
I won't stoop to include the criminally ugly BLR in this conversation. Every part of me is repulsed by the BLR.
Personally, for the game you suggested, my first instinct would be my wife's Marlin 1895 Guide Gun .45-70. A .458 Socom AR might be a fun twist if dangerous bears are on your list. But either of these might be a bit punchy since you mentioned you didn't like the recoil of the .45-70 already (which I find to be more mild than most 30caliber x 2900fps+ cartridges).
A .35 Whelen wouldn't be a bad choice, or a .338-06. Not quite as punishing as some of the heavier magnum cartridges on your end, but plenty of punch to deliver death to large game on the other end.