From EE undergrad to CS grad?

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I studied EE as an undergraduate student and took courses from a variety of subfields of EE, and I am more interested in CS research. I also already worked in CS labs during my undergrad. Considering that I didn't take many CS courses, would it be better to apply for an EE PhD and then work for a CS advisor or should I directly apply for a CS PhD, where I might have lower admission chances due to my lack of coursework in the field?