I suggest you look more into each major.
At some schools CS will be in the engineering college and Comp Eng certainly will be. Comp Eng at many schools is a variant of Electrical Engineering and you’ll take many of the same courses EE’s do but with an emphasis on digital design and CS. An EE major is essentially 4 years of applied calculus so expect more than a healthy dose in Comp Eng.
At most schools it is difficult to change majors into the engineering college, but it’s often more difficult to get accepted as an engineering major.