If you want to work at a company offering more responsibility and/or more money, you consider the company that's offered it to you more favourably than the bigger company that says they like you very much and will decide if you're good enough after a week or two. Especially if you suspect that reflects how the respective companies will respond to any future requests you might wish to make if working for them.

If you only want to work at a big company, you probably don't interview with the smaller company in the first place.