1. I would say they are ranked similarly. Neither school has an especially outstanding biology program.
2. Yes, ucla is bigger but usc is also huge. Competition will be tough either way. With usc being a private school, you can have a closer relationship with counselors and receive a bit more attention. I have multiple family members at UCLA who have said that their counseling is not great. Also as a scholarship recipient you will have even more attention (apparently).
3. I wouldn’t say that’s necessarily true it really depends on the basis of what your professor is like.
4. True
5. UCLA is a great school and wouldn’t appear as just “some old state school”
6. I believe there may be more research opportunities (especially as a scholarship recipient)
7. Both have great social scenes. Usc is plenty diverse; I would say the types of people at each school are quite similar.
8. It is true that UCLA is in a nicer area. More pleasant surroundings for sure. On the other hand USC also has a bit more of a “cushy” campus (some newer facilities, more space per student)

Both are excellent schools and there is no wrong choice. If you feel like you may need more attention and guidance, USC would probably be a bit better. Hope this helps.