After Spock Prime said they defeated Khan at great personal cost, Spock asked how they did it, and the scene ended. It would be interesting to know how or even if Spock Prime answered that question.
The two circumstances are so different I really can't think of anything specific Spock Prime could say that would've been useful. I guess he could've provided his impressions about Khan as a person, and that may have been useful to Spock in formulating a strategy against Khan, but that's about it. In fact, that would be the reason to contact Spock Prime instead of just use the ship's computer to find out about Khan. Spock Prime had valuable first-hand
information about how Khan operated.