I spent the first 17 years of my career at startups and am going on year 7 at big companies. I really think people should experience both. Startups offer the chance to actually experience and solve many of the same problems faced by big companies. This provides invaluable experience in understanding these problems from the ground up and the benefit of learning from doing, even if not building the optimal solution. At a startup, it's often possible to have a larger scope, giving a good big picture view of how everything works from "servers" to data to services to the front-end. You might even get a direct connect to customers and have to deal with org-level problems. Compensation is likely to be lower, but maybe comes with a lottery ticket.
When it comes to big companies, you'll have to deal with many of the same problems, but at a much larger scale and with many more stakeholders involved. Your big picture startup experience can help here (similarly, your big co experience can help you scale startups). Big companies can pay more and offer better benefits. At senior level especially, that pay difference can be significant.
Finally, regarding "the right way" to do things. At the few big companies I've been at, nothing is perfect and systems are so large that they've reached a level of complexity where few people have a solid end to end understanding of things. Rather than learning about how to build and scale systems, many people end up gaining very detailed knowledge about one particular aspect of such large systems.
When it comes to big companies, you'll have to deal with many of the same problems, but at a much larger scale and with many more stakeholders involved. Your big picture startup experience can help here (similarly, your big co experience can help you scale startups). Big companies can pay more and offer better benefits. At senior level especially, that pay difference can be significant.
Finally, regarding "the right way" to do things. At the few big companies I've been at, nothing is perfect and systems are so large that they've reached a level of complexity where few people have a solid end to end understanding of things. Rather than learning about how to build and scale systems, many people end up gaining very detailed knowledge about one particular aspect of such large systems.