Hermione is very mature in outlook for her age and Sirius is quite the opposite, so it would probably even out a little. There are a few times when it could be difficult, for example, Sirius has had so much life experience that Hermione can't possibly understand and that can bring around the old 'you'll understand when you get to my age' argument.

Sirius would love Hermione for her mind, primarily, since they're both very intelligent, and also her loyalty. Her logical rationalisation could be frustrating for her at times, but it would also ground him in the way that Remus does for him at the moment. Sirius loves how methodical and well-planned Hermione is. But at the same time it drives him crazy when she uses that knowledge to correct him or her planning impedes his impetuousness. In the same turn, Hermione loves how he can be wild and dangerous. She loves that he's hard to predict that he acts first and thinks later. But at times she hates when he acts without thinking or when his spontaneity ruins her well-laid plans.

Hermione can be portrayed as two dimensional in canon, but once you read between the lines you can see so much more to her, and pairing her with Sirius seems to bring it out in her. She has both great insecurity and also astonishing self-confidence at times. She also has an awful lot of wisdom for her age and can be very insightful.

Hermione would love Sirius's impulsiveness, even though it would be a source of irritation at time. She'd also love the caring and protective side that he's shown towards Harry in the past.

Her being with Sirius shows more than just her brains and being more mature than Harry and Ron; it also shows that she has a vulnerable side, that she wants to love and be loved by a man. All in all, it makes her easier to relate to. Also, it seems to be a trend that Sirius brings out her lighter side.

Fanfiction gives authors the ability to manipulate these harder sides and bring out their views on just how caring she is under the knowledge. It does give her a new depth because pairing her with Sirius allows the more adult/romantic of her come through because she's not dealing with hormonal, adolescent love like she would be with dating someone her own age.

Their relationship would be an absolute rollercoaster of emotion from the word go. A lot of these emotions would be very contradictory.