You search a place for something. For example, you search your pockets for loose change. You can say, "I'm searching for a new job" or "I'm looking for a new job." Another phrase is "I'm seeking employment."

It's not a question of which one is better, it's a question of which one is correct. 'I'm looking for a job' is correct. 'I'm searching a job' is NOT correct. This is a very common mistake among Italian learners. The Italian word 'cercare' does not translate as 'search'. You can say: 'I'm searching for a job' but you can never say 'search+ object' to say what you are looking for. The object of the verb search is the place where you are looking. For example: The police searched the whole house looking for evidence.

When comparing the terms "Searching" and "Looking" you have to consider the way in which the reader envisions the term. "Looking" is a much more common and informal term in the situation you described. This is because you can "look at" things without much effort involved. When you say you are "Searching for (insert direct object)" it implies a more intentional and involved approach. Therefore, if you are writing a letter or filling out a resume, you will want to use the term "Searching" to sound more professional. If you are just chatting with your friends, either is fine.

It is more common and less formal to say you are "looking for a job".