I've moved here little over three years ago now from Toronto, and I have to say Montreal is much dirtier. But I know the exact causes, at least at the first level for this:

• Medium density renters are less organized than single family or high density zoning: with so many people renting (one of the highest in Canada among the big cities) it has people moving around more often, and they are uncaring about their environment. In contrast Toronto high density often comes with property management, while single family zoning areas, even when the house was converted into multiple units, comes with obligations towards the neighbourhood in the form of bylaws.
• Ruelles are somehow an afterthought: Whether plowing in the winter or cleaning (with a street sweeper/washer truck) in the spring and fall, they are completely ignored by the city, letting residents fend for themselves. This comes back again to transient renters in an area then not really caring about their back yards in medium density.
• Garbage collection is very unorganized: Sure, everyone gets green bins and compost bins, but the actual garbage bins don't come from the city and it's the wild west. In contrast, in Toronto bylaws regulated the size and number of the bins the landlord had to purchase based on the number of occupants. Collection was a lot less messy when it wasn't individual guys throwing various sized bins and garbage bags around, but just pulled it up to the lifting mechanism instead.
• Gravel creates a lot of dust: This is especially bad in the spring when the snow melted, but the city is very dusty year round. Either there's too much gravel use in the winter for the roads or there's not enough space to capture it. I think the city could do better here by just embracing the snow and ice instead of putting down gravel and salt after they did such a good job of hauling away the snow anyway.

But I'm no urban planning expert, so I don't have a more abstract insight into these issues.

Edit: to add, I love Montreal despite all its flaws.