If you want to improve something, train that thing specifically. Obviously, Dips will give you more strength, and that will definitely help as both movements train the same muscles, but if you want to improve Push-Ups, train Push-Ups.
Let's say your max is thirty Push-Ups. If you have the time, do a Pyramid workout. You start at one, and keep adding one Push-Up a set until you get to thirty, and then you reduce a Push-Up a set until you're back down to one. That's 900 Push-Ups. Then, do 3-5 sets of Weighted Dips at about 3-5 repetitions a set. You should see progress.
Although, I'm curious, if you want more strength to improve Push-Ups, then what's stopping you from training a similar, yet tougher, movement like Diamond Push-Ups or even One Arm Push-Ups.
If you said where you are and where you want to be, then you'd get some better advice.