For academic graduate studies, work experience rarely helps, since PhD programs are intended for professorships. One key exception is when the professor/PI in whose lab you are most interested in has hopped in and out of the industry, admissions into that lab often place a positive value on related work experience.

One key assumption underlying my answer is that labs and individual professors have more sway on graduate admissions than the centralized admissions office compared to undergrad admissions.

EE and CS often have significant overlap at many schools, like Stanford. At more theoretical schools, like Caltech, Math and CS have more overlap. Just justify your graduate study with respect to your undergrad work in your statement of purpose essay.