The task has not become easier, the bard just did a super good job. Because of that I think advantage is better. DC is how difficult a task is.

Here's an example of using a lower DC to intimidate a guard.

> Player: Violet looks at the guard. She want so size him up to see if
> he is a tough guy.
> 
> DM: Roll Wisdom (Insight).
> 
> Player: Nice, 18!
> 
> DM: This guard has a big scar over his face and looks like he's seen a
> thing or two in this town.
> 
> Player: Yikes! Violet checks another entrance.
> 
> [...]
> 
> Player: Okay, Violet also sizes this guy up, I rolled another 18 on
> Wisdom (Insight), does she learn anything?
> 
> DM: This guard looks nervous. He looks to his side as he seems to hear
> something. A rat darts across the path. He jumps a little and quickly
> looks around to see if anyone saw him lose his cool.
> 
> Player: Perfect...

Since Violet is about to intimidate a guard who is more easily frightened I'd reduce the DC here instead of giving advantage. *(However, if she still did the super cool stuff with her magic I would also still give advantage.)*