A bit of a random question, but how high do you have the mower set for that and/or do you rake a bit first to fluff the leaves up so the leaves are easier for the mower to get? I have been trying to chop/collect leaves with my mower and its very hit and miss. I usually mow at 5-6" because I keep the grass on the long side (trying to let it outcompete some other shorter stuff) but maybe one shorter mow is worth not having a royally big leaf-collecting job if that's what's needed.
When I use my riding mower for leaf collection, I usually have it set to the highest position, which is all the way up (about 6 inches). If the leaves are dry, they just get vacuumed up and thrown into the collection bins. I have a 3 bin collection system, but leaves will fill it up fast. Also, I have to check the chute from the mower deck to the bins constantly for blockage. The trick is to judge how thick the leaves are on the ground and slow down the mowing so as to not plug up the chute.
Having said that, the bins fill up extremely fast and need to be dumped accordingly. But I find that mowing the leaves, checking the chute, and frequently dumping the bins is still much much faster than raking the leaves in a pile and moving them later.
If the leaves are wet and matted down, I just don't mow them. Wet leaves will immediately plug up my chute. So I don't even bother. But if you don't want your wet leaves to winter over on your lawn, then I guess you would have to take out a rake and work them up manually.
I like to mow my lawn several times in the fall so the leaves never really get very thick on my yard. If there is a patch that gets too thick of leaves, then I mow them down with my other riding mower that has mulcher blades on it. That chops up the leaves into bits and leaves them on the ground. Then I can come back later, if I want, with my riding mower with the collection bins, drop the deck down to normal mowing height (about 2.5 inches) and vac up the bits of leaves.
As for the chickens, I think they prefer the larger leaves rather than mowing the leaves first with the mulching mower, and then mowing up the bits with my riding mower with the collection bins. Of course, the finer you break down the leaves, the faster they will compost. But I have more compost in my chicken run than I need to harvest, so it's easier for me just to mow them up with the riding mower and throw them whole into the chicken run.
I have a tow behind leaf sweeper and collection unit, but it too fills up way too fast and I find it more work to dump the leaves into the chicken run. It is just easier for me to carry each collection bin from the mower into the run to dump then it is too empty the leaf sweeper and then carry the leaves.
I also used one of those extremely large drag behind collection bags for leaves. Instead of filling up the 3 bins, you just have a huge bag that drags behind the mower and fills up. It holds maybe about 5X the amount of leaves that I can fit into my 3 bins. That really works great for moving the leaves into the bag, but I found that the bag was too heavy for me to carry anywhere and I spent too much time having to empty the huge bag of leaves into garbage sized containers to carry into the chicken run. If I had someway to drag the large leaf bag into the chicken run behind my mower, dump the contents, and then drive out again, that would be my best option. But I only have a people sized door to my chicken run so my mower will not fit.
Since I got chickens, none of my leaves get burned or sent to a landfill. I consider them money on the ground and why would someone want to burn money or throw it away? Ditto for fallen branches that I can put into my wood chipper. I will add the wood chips to the chicken run compost and/or use them as deep litter for the coop. I also shred most of our paper and light cardboard from the mail and deliveries so that stuff does not end up in the landfill either. It all makes a good carbon source for the composting.
