TP4056 or LM2596 which is better for solar mobile phone charger?
First of all, you will not be able to generate a 5V 1A output with any of these modules, simply because your solar panels aren't strong enough. Even if we assume you use the (stronger) 9V 200mA one and step the voltage down to 5V with 100% efficiency (which isn't possible), you would only get 9/5*200mA = 360mA at 5V. The real vlaue will be even lower.

But in general, what you want is a simple step-down converter, either with fixed 5V output or adjustable output set to 5V. The TP4056 is not the right module, because it's designed to charge the LiIon battery by itself, but the phone has the charging circuit already built-in. The LM2596 would therefore be the better choice.

But if you continue with the project, I strongly suggest that you use a better solar panel, because at less than 360mA, your phone will charge either very slowly or not at all.