Rabbi Shlomo Aviner suggests that Mesilas Yesharim (MY) be studied before Chovos Halevavos (CH) since MY is a written in a more accessible style and the topics are more basic. CH is deeper and the language is harder.
THinking about it some more with MY you will come away with more actionable tasks. i.e zerisus, zehiros, etc.. with CH the take aways are more in the realm of thought and contemplation (i.e Bitachon, Belief in Gods' unity, etc... )The author of CH calls those things which are actionable "Duties of the limbs" whereas he writes that his sefer (CH) focuses on those traits that are dependent on contemplation - "Duties of the heart" hence the name of the sefer.
I feel that they are both great and you should get yourself a teacher and start right away. you wont lose with either and understanding one book is not dependent on understand the other.