Q: I've been looking for more flexible and easy to customize LMS for our online classes? What are the most competitive solutions on a market right now?

A: After attending the 4th Annual QM (Quality Matters) Conference on Quality Assurance in Online Learning Program I would look closer at products like Canvas: http://www.instructure.com/
http://www.instructure.com/higher-education
Also SoftChalk offers solutions for eLearning initiatives: http://softchalk.com/