With a modem, you get a built, tested and approved line interface.

Telephone line interface design is a specialist area involving high voltages and analogue stuff. It is fraught with difficulties; not least the legal and regulatory ones - in some territories it is ILLEGAL to connect anything to the public telephone system unless it has specific approval. It doesn't matter how well designed it might be; it also has to have the right rubber stamp.

Even if it's not specifically illegal, your telephone provider is likely to take a dim view of you using their capital equipment as a test-bed for your project.
Remember, the phone line to your house is exclusive to you; if anything goes wrong, they know who you are!

Therefore, for connection to a public phone line, you should stick to the modem! (unless you have a built, tested, and approved line interface for use with your own stuff).