They are both examples of mature commonly available laboratory techniques. To claim that one technique is more "advanced" than the other is to ask the wrong question. Rather it is better to ask which is the most appropriate (and available) to the problem at hand.
Yes, Charles H Hocart is right. If you have a mixture of small molecules, hplc is likely to be the appropriate choice. If you have a complex protein mixture then generally, but not always, electrophoresis would be used in preference to hplc. You have to consider your objective first, and then choose the most appropriate technique second. Both hplc and electrophoresis can be great techniques, but there are many others analytical techniques that may need to be considered too.
Since HPLC can answer questions of both small and large molecules even if they are ionized or neutral, it may be mentioned as more universal. Already ionized or ionizable compounds are needed to perform electrophoresis which may be counted as a limitation. But, indeed, in some cases, depending on the application, improved resolution can be achieved at electrophoresis than LC. In my opinion, they must be used orthogonal and complementary (e.g. antibody characterization, QbD workflows)