That first sentence is important.
I've treated both of my plots the same over the years, and they react differently. My one plot is essentially a raised bed with almost full sun. The other is ground level with less sun. They're less than 10 feet apart.
I've been throwing my grass clippings on as mulch for a few years now, the lower plot has had a fungus issue (passed quickly no harm) and the upper has thrived.
I'm currently experimenting with fresh clippings vs some that have dried for a few days. Results are pending. But I can say that weeds are much more manageable with a heavy layer.
As for slugs, in my experience it seems that the mulch keeps them at bay, it's when I let weeds get out of control that the slugs appear. The weeds keep the surface of the soil shady and damp, the mulch gets sunny and dry.
There are so many variables over and above climate, soilt type etc.
For example, we have to distinguish between tilling and no-dig gardening. Proponents of no-dig gardening will tell you that tilling destroys the soil life. So that instantly makes green manures problematic - you can't till them in. The no-dig alternative would be to chop and drop then cover in a layer of compost.
Many no-dig gardners produce 3 or more crops in one bed even in climates with very short seasons. They underplant, have plug plants ready so when one crop comes out another goes in and hits the ground running. Simply putting a layer of compost on your beds once a year facilitates this. You don't need cover crops to protect the soil as the compost mulch is your cover. If you're growing green manure in the bed you aren't growing crops to eat/sell.
So for sure there are benefits to green manures. But you will get great results with no dig and an annual compost layer. If you don't have a need to be producing eddible/sellable crops on every square inch of your land then growing green manure's is a fantastic thing to do - but for the no-dig gardener you chop it down, leaving the roots behind and put the tops on the compost heap.
The point I was making was to focus on the underlying principles that apply no matter how you do your gardening.
1. Soil life feeds your plants.
2. Soil life needs organic matter
3. You can import organic matter (and you need to - or minerals etc - if you harvest anything from your garden and move it off site as you will lose nutrients over time).
4. You can also grow your own organic material. If you chop and drop (or chop and till) all the nutrents go back into the soil so you have net gain. However, you get the same result (organic matter to feed the soil life) by growing green manures on any empty beds and using it to make compost. In fact, this is better as you're taking nutrients from another bed and adding them to the bed you're composting.
You can't say which is best without taking ALL variables into account.