How should I think about levels when it comes to evaluating jobs and in my career overall?

Level and promotion are decent career goals as they're fairly concrete, but I strongly believe that you shouldn't focus that much on them and level should never be your primary objective. Here's why:

• I personally think promotion should be considered a 2nd order priority: If you're truly learning/growing and doing good work, level will come with you. However, it is a nice goal to set (and you should be deliberate about working with your manager to make your promotions happen), especially earlier in career, as it's fairly concrete. If you're working at a FAANG company or something at a similar bar, the level is quite meaningful as it will translate well across companies and you likely won't get down-leveled.
• That being said, level is also kind of a mess as there's no standardization across the industry. There are a lot of people with fancy titles (i.e. Director+) at weak tech companies nobody has heard of. I have seen many of these folks then go to FAANG and get down-leveled 3-4 times: I remember someone who was a VP at a startup coming into Meta as a junior manager.
• In the hypothetical, I would definitely take the lower level offer. At the end of the day, money puts food on the table, not level. And you also will have less stress from the lower expectations. I treat compensation as a 2nd order priority as well, one that's far more important than level.
• There's also a really bad failure mode: You being overleveled and then struggling to perform, which is just a bad situation for everyone, especially if you get put on a PIP. It's not as applicable to your situation as you're at TikTok, but I've seen a lot of engineers go from companies much weaker than FAANG/comparable companies and into these top companies, only to struggle immensely after joining.
• At the end of the day, the best goal for engineers at your stage in career is to just keep doing your best work and push yourself to grow along the way, ideally on a supportive team that makes you happy and enjoy work.

All that being said, getting promoted is a perfectly fine goal to have as a I mentioned before, and we have excellent resources on how to do that:

• "Mid Level to Senior Promotion - What should I keep in mind?"
• "How can I come up with big initiatives, especially those at a Staff level?"

Can you ask where you sit on the comp bands for each level? If you're on the lower end of the higher level, you'll presumably get larger salary increases in the first few perf cycles. And you may also have more success asking for more salary and/or equity.