Suttas are the teachings of the Buddha. The greatest benefit I have found in memorizing Suttas is that it is much easier to reflect on the meaning. If you have memorized it, it is part of you. It can come up at amazing times to help you, especially when you are in need of help, you are confused or you are getting in some difficulty. It is the Dhamma coming to help you at that time. I have had phrases from some of the Buddha's teaching come up at an appropriate time and help me, help balance the mind.
There is one discourse of the scriptures where the Buddha talks exactly about this and how it leads to the final arrival of truth, which is enlightenment. It starts out with respect. Through respect, we go listen to the teacher. By listening to the teacher, we hear the Dhamma. Then we memorize the Dhamma, then we reflect on its meaning. When we reflect on its meaning, energy and zeal arise. When energy and zeal arise, we control ourselves.
Actually even though I haven't memorize it yet, many of our assistants have and I get to hear it so often that I started to understand what it meant. So this is the benefit of memorizing Suttas. By memorizing Suttas, we reflect on its meaning. By reflecting on its meaning, energy and zeal arise. When energy and zeal arise, we start to control ourselves and this leads to a few more other ones until the final arrival of truth.
The Buddha did say, though, that one has to go over and over and do it again and again and again and again. So that whole process leads through cause and effect to the final arrival of truth. You have to practice over and over and over again, so energy and zeal arises continually, so there is continual awareness and that leads to the final arrival of truth.