It all massively depends on your physiology, how much you run/walk per week, how long you've been training, what sort of surfaces you're moving over, what other strengthening exercises or other repetitive routines are effecting your legs and feet, what past injuries and muscular/skeletal deficiencies you have to work around - everything. Everyone is different, trying to be shoehorned (pun completely intended) into one of however many pigeonholes and convenient fads the industry deems necessary.
I got into trail running right around the height of the ultralight, minimal/zero-drop shoe trend and to be honest, it was as much of a hindrance as it was a help. Yep, they felt great on shorter runs over soft/muddy ground, but on longer stuff over rock, roots etc. they were fatiguing AF, would just bang up your feet, wear out your lower legs and kill your stabilisers (though admittedly just building volume does the same). Yes, I read the The Barefoot Runner, did barefoot training intervals and all that... I stopped short of buying Vibrams though... listening to a mate complain endlessly about his on a 30km trail run did not convince me they were a good idea
Same for the original generations of Salomon S-Labs Senses, which were as hard as a rock. It's interesting - and very telling, perhaps - to see things trend lately towards more foam, rock plates, nylon and carbon plates and more comfort, even with shoes that have low drop.
Anyway, that's for running specifically. Trail runners for bushwalking, I feel, simply comes down to comfort, protection and the type of tracks/terrain you're walking. For cleared paths and especially for rock/boulders/scree, trail runners are great and probably the better option. Overland Track, Frenchmans Cap, Walls, etc. all perfectly fine in runners.
For hemmed-in pads and proper off track, the extra toe/ankle protection from impacts, abrasion and possibly snakes is kinda a good thing. While I think the waterproofing aspects of boots is questionable (and negated by sweaty feet) versus the actual ability of most trail runners to dry out in a reasonable time period, there's no doubt that it is easier to keep crud out of boots with gaiters as they tend to form a better seal around the ankle cuffs. If you're doing a walk that involves wading a lot of mud, that's definitely a consideration.
I don't honestly think boots carry a heavy pack better per se than trail runners. I think softer/more flexible soles tend to transmit the sensation of rocks etc. through your feet when you've got a heavier load on. 'Ankle support' is a lie
If you need better ankle support, strengthen your ankles... a bit of material and foam won't do anything. The only boots with ankle support are plastic ski boots :-p
Ironically of all the advantages of boots over trail runners, I've found durability not to be one of them. I regularly get 500-600km out of a pair of trail runners, and generally have to retire them because the soles have worn away completely. Yet have killed almost every pair of hiking boots I've owned in the past five years within 100-350km of use through the uppers - leather or synthetic - wearing out and holing. That's with ongoing gluing repairs to contain/limit the damage. Doesn't matter if they're lightweight synthetic boots or heavier leather boots - they all die the same way. Though I did have a pair of OnCloud boots delaminate their soles on their 3rd trip too... clearly that glue did not like southwest mud.
Now granted, the boots probably see a bit worse terrain than the shoes, but I still thrash my runners through a lot of mud, scrub, against rock and whatnot, and for some reason the leatherette uppers on those survive so much better than they do on the uppers of boots.