Here's my take from my observations in school and work. Physics is the best undergraduate degree that you can get and essentially nothing will throw you for a loop once you get to grad school. However, you MUST go to graduate school because you will have a hard time getting a job if you stop at the BS level. After that, your career options are for all practical purposes limited to government sponsored research (NIST), academia, or small startup tech companies. You might get lucky and be one out of two or three staff physicists at Intel, Dupont or some other big company. The choice of school is important here because of the competition. Do your best to get a degree from one of the top 30 schools and make sure you have at least two full publications before accepting your PhD.
If you consider stopping at the BS level, would like to be in the chemical industry but are undecided about grad school, a BS in chemical engineering is the best degree to obtain. Everyone reports to the BS process engineers in industry since they are the ones responsible for making the company $$. Research at the grad school level in CE basically blends into the same research as chemistry programs. Your undergraduate school as a BS engineer is not very important. Essentially all programs are recognized. If you go to grad school, pick one of the top 15 (Minn, MIT, Cal Tech, Texas, Princeton, Mich. to name a few) schools and have at least one full publication. Contrary to Paul's manifesto, my observations indicate that a PhD in Chemical Engineering is the best option (out of Chemistry, Physics or Chemical Engineering) for job stability at the PhD level.
Chemistry is an unusual subject. Statistically, jobs for BS Chemists are relatively low-paying. Chemistry is also a very elitist subject. If you major in Chemistry and want to go to grad school, do your absolute best to have one of your schools Stanfor, Harvard, Princeton or Cal Tech. There are some real posh jobs (meaning real interesting research that you get paid money to do) at Dupont, Dow, and ExxonMobil central research, however, you must have a "pedigree" to get in.
If it sounds elitist and irritating, it is. Welcome to the world of nerds and egos.