20% Rule.
20% of the time your player should absolutely shine. Player builds a tank? Let him have moments where he shrugs off hordes of little guys, holding the line and being amazing at what he decided to play. Player builds a CC spellcaster? Let him successfully dominate minds, twist the hearts of leaders, etc. 20% of the time your player should struggle. The tank runs into enemies that attack different saves, or a single big brute that forces a tough choice about taking the damage or not. The CC spellcaster runs into a high save enemy, or just one high save that requires attacking a different save than usual, etc.
I don't remember who came up with the 20% Rule, but what it taught me is to let players have their crowning moments of awesome, to not be afraid to throw challenges they might struggle to overcome, and that both of those things should happen in moderation. 60% of the time, everything is normal.
So my answer to the OP is... both? Sometimes the challenges will be tailored to different players, to really challenge them and keep things interesting. And other times there is no increase in difficulty, to give them moments of badarsery. And often, both are happening in the same skill challenge (one person shining, another person struggling, etc). And sometimes the dice gods make their own stories.