According to the ma'amer of the Lubavitcher Rebbe, in this video as explained by R' Manis Friedman shlita (one of our best teachers of hashkafa!), which is certainly based with the entire Zohar and Arizal's teachings in mind, is that we are both.
We are more Hashem's children than our children are our own (because in Kaballah, a child originates from the Sechel of the parents, see Tanya Ch.2). This puts us in an "automatic" or "natural" (so to speak) connection with Hashem. This makes it a more superficial relationship, but is nonetheless true and important. We enjoy the natural love of a Parent and child, the sense of home and belonging, and the immense Rachamim that comes from a Father for His first born son (note, of course, all humans are Hashem's children, not just Jews).
However, Hashem also chose us, using His supreme Ratzon and Bechiras Chofshis, which means that Hashem Himself, b'Etzem, with His entire Self, chose to become ours (Anochi Hashem Elokecha), and we are to choose to be His too. This is the servant-Master relationship (in a marriage, each spouse should view the other as the object of their entire devotion and service, their master). This is a relationship of pure mesiras nefesh, I am for you (not Myself)*, you are for Me (not yourself). Everything I am is yours. So this is the marriage relationship between Hashem and His people. It is much deeper and shalem.
I just want to dwell for a moment on the importance of Ratzon (and may I recommend this ma'amer shiur for more info). When we make a choice using our Ratzon, what are we doing? Assuming this is a true, bechiras chofshis choice, it means that we are identifying our complete self with the choice we make. This is what the deepest realest most essential and complete true me wants, all of me, and what I want is basically the highest most complete expression of who I really am. So this choice is me, and therefore I blur the line between me and Hashem and we can become truly One. (This is what Hashem wants our marriages to look like by the way!)
So the servant Master relationship is the most important one, the one that takes the hardest work, is the most fiery and passionate and complete, and will take us to our true destination and purpose. Until then, don't worry, you are also Hashem's child so even when things get intense in the more important relationship you have with Him, He will never abandon us and will always have infinite Rachamim for us.
* I believe this is what the Ramchal means when he says in Derech Hashem 1:2:1: הנה התכלית בבריאה היה להטיב מטובו ית׳ לזולתו i.e. that Hashem wanted to do good, from Himself (give Himself) to another. He wants to devote Himself to His kallah (Yisrael), that's why He created the world, and of course, our job is to complete that relationship and devote our entire selves to Him! I don't have a source for this, it is my own chiddush which may or may not be correct.