Honestly, they are very similar in many ways;however, the culture is very different.
Similarities: Strong connections to businesses. Strong programs for most business majors. Relatively small schools. Strong emphasis in liberal arts too;thus, they are akin to a "business LAC."
Differences: Bentley started out as a school for finance and accounting and even has graduate courses in these areas. Thus, I would give Bentley the edge if you wanted to major in either finance or accounting. Bentley also is a much more nurturing type of environment with tutors, helpful students etc. Bentley also give a LOT of emphasis on liberal arts. You can take much of your liberal arts, if you want, at nearby Brandeis.
Babson has always been known as an entrepreneural school. If you want entrepreneural studies, they are considered one of the best, if not the best, in the country. In addition, like Bentley, all of their business majors are good.
However, Babson has a MUCH more cut-throat environment among the students. They certainly are not as nurturing as Bentley. I also don't know anything about their liberal arts emphasis.
In terms of admission, Babson is a bit harder to get admitted to then Bentley since they have about 50 points higher in SATs. The average GPA, however, is abot the same , with Bentley having a slight edge.Bentley,however, is known for giving better and more scholarships,which means that it probably would be less expensive in the long run.
Finally, Babson is Babson College. They have only one graduate program that I am aware of: their MBA. Bentley is now known as Bentley University due to a much larger assortment of graduate programs and courses. You might wonder, "why would I care about graduate programs if I am an undergraduate student?" The answer is that you might be able to take some graduate courses while an undergraduate,which will give you more choices. In addition, Bentley provides a number of combined BS/MS programs ,which shortens the time needed for both degrees. Babson generally doesn't have graduate programs.
Honestly, we could argue about pedigree of programs, professor's credentials, rankings etc. however, you would get an outstanding buisness education at either school. Both schools also have very similar connections too. I know that representatives from the Big 4 accounting programs recruit at both schools. You just need to visit the each school and investigate them carefully. Check out other student forums such as "student reviews" forum. Both schools might be similar in many ways, but they have very different cultures.