Bon Ami: I used the Bon Ami cleaner to clean some of the cooking dirt off my stove, and one thing I noticed about it was the very pleasant citrus smell. I felt like it worked just as well as any regular chemical cleaner and did a good job of cutting through the grease. I was really happy about the fact that the ingredients were safe and not toxic. The only problem I had with it was some leftover yellow residue. It was a bit of a bother to wipe away. I checked its website, and each item will cost less than $4, although it's apparently cheaper if you buy it in stores.
Vinegar: I'm a huge fan of vinegar as a cleaning product just because of its affordability and versatility. One bottle of 16-ounce Heinz white vinegar will cost you about $1 to $2, and you can even get it for less if you have a coupon. After I put a bit of vinegar on my stove, the crusty stains dissolved a lot more quickly than with the Bon Ami cleaner and required less effort with scrubbing. Of course, there is the vinegar smell, but it eventually dissipates after a while, leaving you with an odorless kitchen.
The clear winner: vinegar, vinegar, all the way! Although I think Bon Ami is a strong contender, vinegar definitely wins this round.