You intend to apply for a competitive major where GPA is critical. The downside of 13-14 units is you might become a bit lazy and miss a chance to nail an extra class towards requirements in that semester. The downside of more units is that, if you find after the drop deadline that you are still seeking the groove at college, a common experience, then you risk your GPA. Which is worse to you?
The reason the advisors suggest a lower load is based on evidence that in the first semester at Cal, those with regular or high loads earn a lower GPA than the rest of their college career. There is a lot to adjust to, it is not just a matter of mastering the subject.
Since most who enter have been near the top of their classes and easily earned high grades with heavy workload, it is quite a surprise to find that grades here follow a distribution that will put the majority of you into the B, C, D or F territory for the first time. Because of the curve, you will not realize this in the first weeks of class when you are learning all the concepts. It is when the first midterm hits and you discover what grade you get, then compare it to the posted cutoffs for various letter bands, that you realize that this is not high school any more, even high school with lots of honors and AP classes.
Anyone who enters with AP unit credits already has a buffer against the 15 unit per semester average they will need to earn to reach graduation in four years. If you have just one AP that produced 2.7 units of credit, you can start with 12.3 units the first semester, hit 15 every other semester and get to the full 120. Most have more AP credits than that. Why not take the advice?