You earn through both the YouTube partner and monetization process, but the latter is quite easier, while the processes for the former are quite stricter. With YouTube partner, you will have to apply for it; while monetization is by invitation immediately, you have a video that has gone viral enough to worth it.
YouTube partner actually has many more benefits that are attached to it, but not much people are involved in it like monetization. With YouTube partners, you gain more than just earning on your videos, but you also have the chance to promote your own videos through Adwords.
YouTube partner looks to be of more benefits than monetization, but at the same time, you cannot afford to let go of monetizing your posted video. YouTube partners will require more time and resources, but you can still apply for a YouTube partner later when you are ready.