In Wikipedia I found that machine learning is a subsection of neural networks science. So, does it mean that work with machine learning is itself implies working with neural networks or not? What will be better to use for pattern recognition tasks in terms of efficiency and complexity?
Machine learning is a part of neural network? I'd be surprised because machine learning includes dozen of techniques that have nothing to do with neural network. It's most likely the other way around.
The exact pattern recognition algorithm depends on your requirement and data set. There're many such algorithms, for example, SVM, linear models for classification, HMM, PCA etc. Note that the phase "pattern recognition" is a very general term, there is no algorithm that always work. It all depends on what patterns you are looking and what kind of assumption you can make.
I recommend Dr Bishop's "Pattern Recognition and Machine Learning" book, you'll learn a lot from the book.