The Homepage, not the social media profile.
A homepage is like a home; it shares in all the qualities and eccentricites of its owner. The decorations are in a way that reflects his character; there's collections that relate to his interests, there may be photographs of people and places important to him. These are all arranged in rooms, in their own unique way that make sense to the owner.
Perhaps this is why webpages are more fun to browse than social media pages; they are truly particular.
Contrast with social media. Entirely owned and maintained by a company to algorithmatically hold your attention for the longest time that they may earn the largest profit. This motive has impact even on the design of social media profiles. Naturally, such a single-minded drive designed to appeal to the majority of people in the majority of places will result in the ugly, sleek blandness of social media profiles.
Even the name 'profile' as compared to 'homepage' has echoes of law enforcement, a 'profile' on you where your habits and deeds are recorded forever, sold and shared, beyond your control. A homepage has exactly what its owner wishes it to have; no more and no less.
A homepage also doesn't force self-identification, but respects privacy. A personal website has just as much of the person revealed as he wishes, unlike social media where he's under constant pressure to reveal as much about his life and personality as possible. What he won't supply himself can often be filled in from friends.
Moreover, a homepage requires great personal effort to create and then maintain. Since so much thought and effort must go into a webpage, this gives an incentive to raise the quality of webpages. Unlike a social media platform, where the pressure is to share as much as possible and as often as possible. Half-finished thoughts and opinions formed under rage (that would normally subside in time) florish on social media. This raises 'engagement' much to the shareholder's delight.
Finally, remember that everything posted on social media is owned by that company. This includes your blogs, videos, photographs, conversations. This is surely a sinister thought to consider; you revoke ownership of your own image and likeness. While your creations on your website are free to be licenced in any way you please.