In short, let them play the same class, but check that they play different characters.
It's not a class problem
You mention that you were worried they might compete for the same role, this is something to look for and you know that already. But this is not so much class problem as it is a player problem. For example, if two players want to be the face, it doesn't matter if they are both bards or if one of them is a bard and the other a sorcerer. It matters that both players are trying to do the same thing at the same time.
What you should look for while they create their characters
Talk to them and check these things:
- That their personalities are different. Similar background, classes and skills can make vastly different characters if one decides to be nice with others while the other decides to be an egotistical yet compelling thief.
- Similarily, make sure the way they approach problems is different. One bard may want to talk to people while the other may try to trick or cheat his way out.
For those first two points, look at their backgrounds and what they tell you about their characters.
That their specialisation is different. One bard might prefer to be a storyteller or mediator while the other focuses on music. One might favor diplomacy while the other favors performance and sleight of hand.
For this point, look at their skill proficiencies, stats and spell selection.
Make sure they have mechanically different roles. In combat, they would ideally have two different battle plans. One might want to kill while the other wants to facilitate kills or protect his allies.
For this, check their spell selection and weapon of choice.
Redundant classes is rarely an issue by itself. Especially in 5e, where party (class) balance is less important than it used to be. And especially with a class as versatile as the bard. Even those tools they will have in common work well together; more bardic inspiration just means more opportunities for skill challenges. Being charismatic just means that your social challenges can be more diverse.
In case they play the same character
And finally, in case they play the same character, make sure both know about it and they know what they are getting into. You might find the players will play off of each other's roleplay and become in-universe friends. Or they will incorporate the rivalry into their roleplay. Again, the players need to know what they are getting into.
If they do make similar characters, check up on them after a few sessions. If one of the players feels bad about the situation, you would do better to change the characters before the tension seeps too far into the game.