Let's consider a simple European call option. In practice, the way the Black-Scholes formula is used to price it is by injecting all of the parameters and paying special attention to the volatility and the dividends where their implied values are used. This gives then, by definition, the market price of the corresponding call option.
Now, suppose one wants to price a call option with maturity $T$ and strike $K$ that isn't found in the market (and hence has no corresponding implied volatility or dividends). One could either interpolate between the prices of the options with the closest maturities and strikes, or one could interpolate between the implied volatilities and dividends corresponding to the closest maturities and strikes and then inject into the BS formula.
Which one is the best approach ?