BlazBlue Continuum Shift II - the extra story chapters (unplayable) give good background to Noel, Tsubaki and Makoto's friendship (although, due to the time loop, Noel flinches whenever anyone says "obstacle"), and Kokonoe, Relius Clover and the Nox Nyctores.
The extra info gained from the extra arcade characters is also interesting for BlazBlue fans. My one complaint however, is that I'm finding - at least on the 3DS version - that at times the background music (especially Gluttony Fang, Hazama's theme) drowns out the dialogue, regardless of how low you drop the BGM/how high you rise the dialogue volume.
The only other fault I have with it is the advanced/beginners control system from the first CS (here referred to as technical/stylish). The easy specials system in BlazBlue Calamity Trigger (the first BB game) was a lot more useful, as there it allowed you to get used to the main controls (which is what CS calls advanced or technical).
If you haven't picked up CSII, then I would leave it in favour of CS:Extend, which will have the extra story modes and arcade characters plus Relius Clover.