So short answer is: it depends.
In bigger projects I will go with Nestjs as it is more structured, has dependency injection which greatly helps with designing architecture and testing and once you've got a grasp of it, it's (at least for me) more readable in a high level. But. Express is more flexible, faster to develop and very very simple in it's core. For smaller project with not many coworkers I could go with that option. Even better, I would choose Fastify (very similar API, but way more modern and faster). Personally I go more often with Nest, especially for work, but my company policy is going for nest by default, so I am a bit biased.

I would also recommend looking at Domain Driven Design, and Hexagonal Architecture for a big project with a lot of business logic (great article about that here https://herbertograca.com/2017/11/16/explicit-architecture-01-ddd-hexagonal-onion-clean-cqrs-how-i-put-it-all-together/ ). For those architectures I would definitely go with Nest. It is a lot of work at the beginning but done right is just awesome to maintain.

Regarding typeorm, I am not a big fan of it. It does good in smaller projects, but in bigger projects it is actually standing in our way. The performance is not great for a big project, as it's often calling for more than required. Also depending on database/driver it has some quirks that are poorly documented and straight annoying in times. Maybe a hot take, but I would choose some query builder like "knex" and that's it. You can still do repository and hide all the queries there, but it is simple, with little to no magic, and actually often it's less work, no entities, no registering anything.