As of the advent of the 21st century teaching and learning paradigm, the word "traditional" is a bit taboo. We are expected to break away from traditional teaching models and become facilitators, rather than instructors. However, this has not quite been the case in EFL OR FL language programs because the current research intends for regular classroom teachers to have every resource available in the classroom for the purposes of differentiation, and not enough focus has been placed on ESL learners. In fact, we have a myriad of "quick fix its" that assure fast results per purchase. Unfortunately, not enough qualitative research has been placed upon EFL/FL programs, and not enough quantitative research is available to determine whether those countless and new "hip" language programs are indeed effective in terms of accuracy, retention, and the very important aspect of inferencing, which is prime when learning a second language.
That being said, the two teaching methods that your question addresses can basically be labeled as "the old and the not so old."
In the past, we believed as educators that the way to engage the senses in the process of language learning was to have the students "hear", "see" and "repeat". This was evident in how many spelling and vocabulary words we would assign students to memorize. When Stephen Krashen (1987) provided us with his "natural language" and "monitor language" hypotheses, he basically stated that we were wrong because language is acquired in two different ways: Casually and formally. THAT is the difference between the two methods you ask about.
The cloze-filling, rote method was the traditional, old school way. As I explained, it involved repetition and quick recall. It left out mannerisms, culture, intonation, and inferencing.
The CLT method (Communicative Language Teaching) filled in those gaps way back. It was one of the first methods that advocated for open dialogue, and allowed mistakes to happen. It is a quasi real-life approach in which the teacher basically talks to the student in the target language (a la immersion) and has the student talk back using as much of the target language as possible. Special emphasis is given to personal life experiences and situations that are relevant to the student. It is way more effective than the cloze/rote method because the student is actually engaged in the process, and the engagement causes the student to maintain focus.
These days we know about extensive reading, blogs, and technology as the best ways to casually learn a target language because in the process of trying to understand a situation the student has to problem solve and infer. THOSE are powerful cognitive tools that lead to acquiring and storing information in the long term memory.
Hope this helps!