Training at 4-6, the AI does something interesting: Each character has a "personality". Ein tries to hold A LOT, Zack taunts like there is no tomorrow (etc). At 6, I noticed the introduction of other mechanics into the repertoire drowns some of this out, but it still happens.
I don't know if this holds true on 7 or 8, as I have never tried, I suppose it does, but training on lower difficulties, such as 4 or 3, can give you good practice on reacting to certain behaviors without the AI wrecking you for mistakes. For example, chose to fight against Ein on 4 or such to practice reacting against flawed counter holds. Or pick a character you are not familiar with at 3 and practicing blocking their strings. AI sparring in free mode, IMO, is very good for situational training. You can also just go into free training and establish some conditions, like always stagger escape at fastest or always try to hold at fastest with a random hold. Throw breaks, etc. and see how you fare, see for what you fall and see what you can punish.
Also worth noting: If you just picked up a character, take the time to learn what their safe and fast attacks are. This helps a lot... I felt instantly comfortable at level 6 with Rachel after some research, whereas I still struggle at level 4 with almost everyone else.