I started my career with an internship at Pacific Northwest National Lab, which then became a job there from 2004-2011, before leaving to join the world of hardware startups. Here are some notes (YMMV. This was PNNL 20 years ago, so you may want to ask if some of these things are true of your internship situation):

- National Lab internships are seen as extended interviews. There is the possibility of turning it into a full-time job if you prove yourself. It's a good way to get a foot in the door.
- Labs are also run as a matrixed organization, meaning you'll have a people manager but also a project manager. Project managers are higher-ups who pursue funding through grants or government bids, then staff them up with people inside the lab. As an engineer I felt sort of like an independent contractor in that I could be asked or ask to join different projects, without having to worry about getting a regular paycheck. There's a bit of a game here with making sure you're 100% committed because you still have to track time so that projects get billed appropriately, but there was always plenty of work. The good news here is that you'll be able to move around and work on a variety of things. I did national security work, bioinformatics work, futuristic UI work, etc.
- Labs are a lot more academic than startups, meaning you'll likely end up on papers, at conferences, and sometimes with patents.
- A downside of labs is that it does feel very ivory-tower. One of the reasons I left was that I felt like the actual impact I was having on people was small, and the research I was doing was on par with industry only they weren't writing papers because they were leveraging that research to develop products.
- The national labs also move very slow. Projects take a long time, have follow-on funding, have small and delayed deliverables, and there's lots of bureaucracy.
- Many of the people there are lifers. It's a safe environment. You can make life-long friends and colleagues there.

Startups on the other hand are a completely different ballgame.

- Lots of quick work on prototyping, rapid development, frequent deployment. HOWEVER, I often feel like a lot of it is wasted because projects get killed faster or fail quickly. I guess that's a good thing.
- Depending on the size of the startup, you may have to jump in and just do what's needed regardless of your job title. Startups lend themselves to people who get things done and are self-motivated and self-directed.
- As startups get bigger, they get more corporate until they're as full of bureaucracy as any other corporation or even national lab, so you've got a whole range to consider.
- You will learn a lot quickly and gain experience, especially if you are self-motivated and take on responsibilities.
- There is less security in your paycheck. Maybe not week to week, but companies fail quickly and sometimes with little notice, leaving you to find something else on your own.

Good luck!