“better in terms of the specific program that I am looking for”
If you are confident that you will stay in this major, and if finances are the same either way, then I would go with the stronger specific program. Graduate schools will be aware of the strength of other programs in the same major at other schools.
Also, I agree with @Dustyfeathers that how and what you do is going to matter more than the school that you came from. My experience at a highly ranked graduate school is that the other students there came from a huge range of other universities. What they had in common was that they had all done very well wherever they had gone.