Which one can write a recommendation that is specific about your qualifications and abilities?
A brief anecdote: I was on a search committee where someone had a recommendation from a big-name person in their field, someone widely known outside of their field. At first glance, the candidate's personal connection to this person was impressive. However, the letter body was a single paragraph and light on detail. OK. We had to read the other letters to get the detail we wanted.
A big-name recommendation may get the attention of the hiring committee reading your applications. However, because they're ultimately evaluating you, the level of detail in that letter will matter more to many evaluators than the name at the bottom. Someone still up-and-coming may not initially grab the attention, but if they write a more specific letter, that may ultimately be to your benefit. So if you have two open slots for recommenders, include both! If you're choosing between one or the other, it comes down to weighing relative risk, since not every hiring committee will respond in the same way to your set of recommenders.
To give an idea of a typical balance of letters, I defer to Karen Kelsky, who runs the advice site The Professor Is In. To someone who asks about the mix of recommenders three years post-graduation, she says:
In the end, a balanced roster of letters at three years out will include your advisor, a well-known person who knows you as a colleague or collaborator, a senior colleague from your department who will provide a detailed teaching reference, and—assuming you have space for four letters—one of your other Ph.D. committee members who has also stayed up-to-date on your post-grad-school life.
Note the mix. "A well-known person" may well be one of your "big names," but could also be someone up-and-coming. A "senior colleague" may be a "younger, more hot-shot researcher" in your department, or a "big name" approaching retirement. As long as these people are a mix of people familiar with your work, debating the relative stature of the "well-known person" or the "senior colleague" is small change.