I am currently in a university which is ranked 30 in chemical engineering by US News. I would like to pursue in a higher ranked university something in top 10. But my only concern is that I am now in civil and environmental engineering and have been offered a PhD in my school for admission in chemical and biological engineering relating to stem cell expansion and differentiation topic. If I continue I would be done in another 3.5 years but if i apply to a top 10, I do not know what my chances are getting into school because of my background. Also, it would take me a longer time if I get into it(maybe like 5-6years). I love this topic and would like to work in this area. I am at cross roads if I should accept my offer in my school or apply to top 10 schools next fall.  Also, I am wondering at the PhD level, how much does the school matter?In the sense, is it worth to go in different topic like bacterial culture (which I am not so interested in as compared to stem cells) in a top 10 school or go for this subject in a 30 ranked school?

I should have said that in a better way but what I meant was that I have been working with this prof in chem engg for about 1.5yr unofficially while I have been doing my masters in civil. So, I talked to this prof about the time it would take if I were to continue for a phd and he said it would be about 3 to 4 years. He said typically for a fresh graduate it should be 4.5 to 6 years depending on the person. I have looked up at the websites and talked to friends of these top universities and the trend is more like 5 to 6 years. So yes, they should take the same time but in my case I can save time if I do it here. From a research point of view, I know the department and the prof has good facilities for the work I intend to do by looking at his funding and publications. What I am concerned about is in the eyes of the employers, do they have a bias towards students coming from a top ten university or do they view strictly from an individual standpoint like looking at the student's ability, his publications, internships etc.? In other words, what is the gap from an employer's viewpoint of a person coming for harvard against a person coming from rpi? If someone could throw more light on this, it would be very helpful.

Preference is of course given to someone coming from top 10. Basically it'll just get your foot in more doors, but no company will hire you just because you come from Berkeley, publications, patents, research are far more critical. Anyways, its always frowned upon to do your PhD at the same school you got your B.S. especially if you are working with the same P.I.