I've worked for both types of companies, and I prefer product companies.
But that's possibly a matter of preference.
Consulting is more dynamic and you're exposed to many different projects and probably to many different technologies. I had a good time doing it, but it was for a very good company which is remembered by all former employees: DEC (Digital Equipment Corp.) DEC was acquired by Compaq, which in turn was acquired by HP.
You need to travel and your work place and team is constantly changing, as you work at the client's office usually and teams are determined by availability and budget.
If you work for a big consulting firm, chances are that once you leave a project you won't come back to it, and that can lead to solutions that work in the short term to meet the project deadlines, but are otherwise bad solutions for the long term.
Practices can vary greatly among different consulting firms, some will treat you well, others will simply sell warm bodies as you point out.
Working for a product company means having less or no travel at all, and a stable team to work with. It means also having much better care for quality and long term planning, because you or your colleagues will also be taking care of bug fixing and new features.
You're in touch with the business and the day to day customer issues and needs, which brings a greater understanding of the system you're working on.
However, the technology stack will be less diverse for obvious reasons.
Culture fit is also much more important as your team is not likely to change for a few years.