First, of course you can often use either of our two products in many cases. We do compete!
Second, I think we focus on subtly different customers. There are cases where they're a better fit and cases where I'd assess us to be a better fit. For example, Stack Auth is pretty closely aligned to the Next.js ecosystem. They're really quite strong at serving Next.js. They also have a billing and payments product that's likely interesting to companies with a heavy self-service motion. On the other hand, Tesseral serves only B2B software, and we're not as focused on Next.js (SDK currently in the works). If, for instance, you have a Go backend and sell large enterprise-y deals, we're probably a better fit.
But this will probably evolve over time. I'd expect this comparison to be outdated within a few months.
Overall, I expect our companies will drift in slightly different directions over time. We're both very early stage companies that have focused on pretty foundational features so far.