However, I have to say my experience in software engineering is mostly on SaaS companies, so perhaps I'm just seeing the grass greener at the other side of the fence. Is there any huge advantage of SaaS companies I'm missing?
Not sure why this would be a selling point besides the plain information of what kind of product you'll be working on. The tech stack at SaaS companies is usually relatively modern, but more often than not the code base / system architecture is a clusterfuck that has been growing for years.