Lua has a very minimal string library that doesn't include basic things like escaping and interpolation. It doesn't include regex. I understand the choices behind these decisions and don't disagree with them. But what it means is now you're not just embedding lua, you're embedding lua, vendoring extensions to the standard library, and selecting a regex implementation compatible with your expected runtime and distribution method.

Tcl is built around string manipulation, it's the main and, for a long time, only data type. It has regex built in, a full set of string manipulation functions, and an interpolation primitive.

It's not about what's better. They are both full blown programming languages and you can implement any behavior you care to. In lua you have to care to implement string functions if you're going to do anything complex with strings. Tcl comes with them. That's all.