Can you help me decide between IC at Capital One and senior manager at acquired startup?

I have a choice to make between a senior manager position at my current company and a senior engineer position I was offered at Capital One. Both roles could take me toward my goal (management track in large, quality tech companies) but from different directions.

I could take the senior manager position at my startup-like small company (we have been bought out by a very large company but still operate fairly independently), though the work of moving ahead in my management goals is mostly on me -- to know what management interviews are looking for and to try to work on those things. The company doesn't really do much structured management (e.g. I'm the only person who does one-on-ones with my reports) and I don't currently get any coaching on management or one-on-ones from my own manager (who is not even a software manager but part of the business side of the org).

Or I could go to Capital One and (it sounds like) have a manager to work on my goals with and lay a good foundation for both technical and leadership experience, and also grow my network in a large tech company. The main concern is just that I'm not sure if I'd get an opportunity to get into people management again, if promotions aren't as readily available as they have been for me. However, Capital One does seem like a company that really tries to grow and promote its people. This is my first offer I've ever had in a large tech company and it seems like offers like this might be hard to come by for a while because of the market.

Any thoughts on the pros and cons of these options (including in this market)? For context, I have never worked in a big tech company or large tech company before.