Same TCP connection for two protocols

If you use a single connection for two protocols you would have strictly speaking only one protocol because your client has to decide which kind of data handling has to be used and this decision is defined by the protocol.

If the two protocols are not standard ones but defined by you just combine them into one. Each protocol usually has some kind of header that contains information about the following data. Define such a header that indicates if the data are text or binary.

When using standard protocols you can do the same. Define your own protocol with a header that specifies the type of data.

Using a single connection should be simpler than using two connections regarding the code. Creating and parsing a header requires only a few lines of code while handling two connections is more complex.

So I would go for this solution according to the "Keep it simple" rule.

However, there may be situations where using two connections might be more appropriate. See for example FTP which uses a control and data connection.