1. I would say choose the company that fits what you want/need especially at this point in your career when you are 35+ with 20 years of experience. Put yourself first. Now you are saying that you are much bette at hands on. Then choose the company which provides you that option. I am guessing the company B in your scenario. Of course there is an element of risk involved in a startup but then again, no risk no reward. You don't want to be miserable in a job at 35 which you don't like.
2. The other side to it is that in a large company, you will definitely have the opportunity to meet a lot more people (talented and otherwise:) and perhaps build a great network. How much do you care about that at this point in your career ? You have worked for 20 years and I assume you have a good network already. Yes u can always do more but may be thats not as critical at this point.
Hope this helps and gives you some perspective.
I can say definitely that the large company will have more bureaucracy, which will on more than one occasion drive you crazy. Like you said though, they have the scale and complexity for interesting problems. They also have the budget to fund IT.
Regarding the part about being the most experienced. I don't think that matters, so long as you're still learning. If you're willing to learn from less experienced/less senior people, and they're willing to speak up about what they know, then it doesn't really matter.
My biggest problem with "hands-on" is the same as been discussed ad nauseaum here and elsewhere. It's really a subject for a different topic. I am very good at it, I like it, I am just not sure how long I can keep doing it. I already feel like I am not as fast as I was 10 years ago, but it's a small drop off that is more than compensated by experience. I am concerned about 10 years from now and still doing ops at a hands-on level. I am not sure I'll be able to keep up with 20-year-old at that point. Anyway, I digress. Thanks again.