I can speak from my experience:
My PhD advisor was a tenured faculty member with an endowed chair. He was well-funded and had many collaborative projects with other big names at the university. It was a large laboratory and there was ample instrumentation and expertise available (several postdocs and a number of advanced graduate students) and a lot of groundwork already laid. This environment was conducive to productivity: to date my graduate work resulted in eight peer-reviewed journal articles with me as primary author, plus a smattering of contributory efforts.
My post-doctorate work was with a very young faculty member without tenure. She had practically no funding (outside start-up grant), no existing equipment, no pre-existing ground-work laid, and I was by far the most senior person in the lab (other than her) in terms of research experience. This environment also was conducive to productivity: in my two years there, I published another three first author papers plus again a few contributatory efforts. This in addition to helping to get a lab off the ground.
The point? You can be successful in either environment, but both of them have good parts and bad parts.
If you join an established professor's laboratory, you will benefit from pretty much having a project that has a high chance of success right out of the gate. You will have lots of help from other laboratory members when you get stuck. And publishing is far easier - it's no secret that half of publishing a paper is who the corresponding author is. Your professor can also open doors for you to get a post-doc, because he or she will have a large network of contacts. There's also a lifestyle benefit here - often the tenured faculty members aren't quite as micromanaging as the new faculty members. You have a little more breathing room, a little more freedom to explore on your own what you want to do without your boss hanging over you doing a cost-benefit analysis. On the other hand, don't expect the tenured professor to have much influence on your scientific growth. Sometimes it can feel a little bit like you have no project or structure at all, and they've been out of the lab so long that as you enter your third and fourth years you'll find yourself rolling your eyes at some of their experiment suggestions - "Maybe if you try that reflux on a leap year, you'll get a better yield!" - which you have to take anyway because they'll keep asking you about it until you do it. Tenured faculty members often rely too much on their grad students to come up with all the ideas. But the biggest drawback can be that tenured faculty members don't always have the same drive to publish as a the new guy in town. My post-doc advisor was ready to submit a manuscript practically before the ink had dried on the paper; I still have a paper or two waiting to be published from my graduate work, and that was the better part of a decade ago.
The junior faculty member will be all over your ass from day one like white on rice. Long, long hours, and what pressure they feel, you feel. Junior faculty members are often cranky as hell, and there's no job security - for you or them. If they don't get tenure, you're hung out to dry. And since there's no existing work on which to base your project, other than their One Great Idea, there's going to be a lot of trial and error in the beginning. On the other hand, they'll probably be in the lab with you, and since the success of your project is life or death to them, they have every motivation to help you succeed. Some people rather like this kind of hand-holding; other people can't stand it. Finally, the tenured faculty member is kind of a high-risk/high-reward scenario. There is a larger chance you'll end up diving off a sinking ship half-way through, but if you're the one who's there when the next Chad Mirkin or Robert Langer gets tenure, well, you're probably set for life. In that sense, if you're going to select a new faculty member, you're better off doing it at a highly rated institution, where pretty much every faculty member is going to have a good pedigree. This is less important for a big name professor. Everyone will know his name, and no matter that he works at Podunk U. Still, in the lab of a young faculty member, you're more apt to feel like a big part of the success story; at an establish lab, you may feel like just another cog in the wheel. A big, impressive, noteworthy wheel, but just a redundant gearshaft nonetheless.
In the end, as I said, what is most important is to select someone that fits your interests and your personal style. I'm the kind of guy that likes the freedom to do what I want without someone wanting to meet with me every day to know how I'm spending my time. The tenured faculty member gave me that kind of environment. Other people flounder, though, with that much freedom. They want a guiding influence and would prefer to work closely with someone else toward a pre-defined end, and don't mind working 300 hours a week with someone staring over their shoulder. Being a post-doc is a little different, though, and I think working for a new faculty member was great as a post-doc, since it gave me some insight into building a lab from the ground up. I'm not sure I would have been ready for that my first year of graduate school, though.
All things being equal, it's probably wisest in the long run to choose someone well-established to start your scientific career. You'll most likely publish more papers and have someone to open doors for you down the road. But that's only worth it if you finish, so that's why I say to evaluate your own working style and your research interests and make that the priority. Don't put all your eggs in one basket, either. Have TWO professors you wouldn't mind working with no matter where you apply, because sometimes you don't get your first choice. Importantly, talk to other people in the labs you are interested in and get their take on what it's like working for that person.
So: you can be successful no matter what. But one more piece of advice, if I may. Do not, DO NOT, wait until you're a fifth year graduate student to figure out what you want to do next. Figure that out now. This gives you a goal to work toward. A lot of people go to graduate school because they have no other better ideas. This is a recipe for disaster. Have a goal, work toward it, and be happy. Particularly the last part.
Hope that helps.
(Do note, these are generalizations. So you might encounter a new faculty member who is not cranky as hell. I've yet to see one, though.
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