I’ll speak for Penn here.
In terms of social culture at least, these two are probably very similar. If partying and Greek life are your thing, you’ll definitely find a huge crowd of people here that do that very often.
As for what you’re learning, if you’re not sure, I know Penn offers a lot of flexibility to study different things. You can be admitted to the College of Arts and Sciences and still take classes in the Engineering school, Wharton, etc. I would also say that despite there being more students here than Vandy, the class sizes are relatively small, especially as you move up in seniority in the school.
On the topic of competition and wealthy people, I’d say there’s a lot of that if you’re looking for it, but the school has so many students from different backgrounds that you’d never really experience those things if you that wasn’t your thing.
If you are into the competition though, there are definitely companies that only (or more often) recruit here, which can be a huge advantage for you.
If weather is a big factor for you, don’t apply to Penn haha. Any school in the northeast is submerged in cold for most of the school year haha. And, yes Philadelphia is super diverse so you’ll find awesome Asian food here.
As for prestige, like other ppl said, I wouldn’t really base your decision off of that. If you’re accepted into any of the T14 schools it doesn’t make too much of a difference to employers/grad schools. Although I would say that historically and achievement-wise, Penn would have more prestige just being consistently ranked as a top school in the world and as an Ivy.
Ultimately, these schools are similar in many aspects, but depending on what you wanna do there may be advantages in coming to Penn and the northeast! Good luck on your decision.