They both stink, grow old and fall apart.
I had the wonderful pleasure of taking about 30 bags of decaying yard waste to the dump. I would say you haven't lived until you've smelled the sweet aura of decaying grass, but that would be a complete lie.
How did things get so bad? When I thought about it I realized I only produce 6 bags of grass per mowing, that means that I went 5 weeks without taking this grass to the compost dump.