I don’t think anyone outside of the admissions committee at UCSD can really answer this.
I’m sure they do consider personal statements, but I don’t know if it’s weighted more heavily than anything else, could make up for other significant deficiencies in the rest of the application, or if it’s given much greater consideration than it previously was. All I can say is that you can look at what UCSD says they consider when reviewing applications (http://admissions.ucsd.edu/freshmen/eval-process.html), and I think it might mean something (all though I don’t know how much) that the first four items listed are academic (GPA, test scores, achievement in A-G courses, and ELC). Personal qualities are considered, and this is likely where the personal statement is considered. So I don’t think it’s more important than any of the other things they list, but I think it is still considered, just like everything else. My gut feeling is that the personal statement might become more important in borderline applicants. In applicants who are stellar (in academics, extracurriculars), the personal statement might be less important (unless it’s really bad or alarming in someway), and likewise, in applicants who have shown very poor academic achievement and seem like they might really struggle at UCSD, the personal statement is probably considered but is unlikely to “save” an applicant. But that could be completely and totally wrong.