First, congratulations!
Second, both schools are amazing, and I don’t think you need to worry too much about “prestige” because both schools are very well-regarded by those who will need to know (grad schools, etc.) and relatively unknown by random people you meet on the street.
I will comment only about Williams, since I am the parent of a current student there but have no direct connection to Kenyon. I will try to answer your questions as best as I can.
Pre-professional focus in classes: The qualifier “in classes” is interesting. Being a liberal arts college, its classes are not pre-professional at all (except if you take certain one-month-long Winter Study courses offered by alumni in finance, etc., although there are plenty of purely academic Winter Study classes as well. Winter Study is different.). Take a look at the course catalog online. As far as overall atmosphere- it is a pretty intellectually oriented place, with lots of great discussions going on not only in class but in dorms and dining halls. That said, there certainly are a lot of ambitious students looking into internships starting with the first summer after freshman year.
Athletes: There are many varsity athletes, but they do not dominate the culture. To some extent, there is a divide. For example, in one entry I know, there are 38 freshmen, 9 of them are varsity athletes, and of those 9, 5 are usually active in the entry’s social events, but 4 are not; the 4 who are not are all male helmet-sport athletes, who were so busy with their teams that they participated in very few entry events at the start of the year, and therefore tended to form their main friendships outside the entry more than in it. The freshmen who were most active in organizing most of the entry’s informal gatherings at the start of the year were not athletes. The kids support one another, going to one another’s athletic matches, dance performances, concerts, and shows. There are lots of kids with lots of different interests, and a lot of different activities happening on campus. So, on the plus side, there is not the dominating “athletic” culture you fear. On the minus side, there is somewhat of a division.
Diversity: It is great. Kids from different races and socioeconomic backgrounds and family backgrounds and interests really, truly interact and become friends.
Leadership and professors : you will have similar opportunities to assume leadership of clubs at Williams (some freshmen are already in big leadership roles) and to interact with professors (class, office hours, dinners, events around campus, research).
Traditions, alumni connections, tutorials, Winter Study, endless resources, “impressive” peers— Yes, you are right, these are awesome. And do not forget the numerous clubs, the freshmen entry system, and the Ephventures programs, which make it so easy to form friendships right away!
Cost: You have a great merit scholarship at Kenyon!
Good luck in your decision. Two great options!