I think they both have an important place in your strength training program. Push-ups and pull-ups are obviously excellent body-weight excercises. But body weight does provide a set resistance, and I agree with the answers that suggest that to achieve significant levels of strength fitness it will be important for you to include resistance equipment. Although Chuck Norris won’t agree. His Total Gym is an excellent machine, but it does allow for a progressive increase in resistance by increasing the incline of the bench.
I also agree with Joanne is that whatever you do, find a program of resistance training, whether with body weight or equipment, that you’ll enjoy and stick with.
Good luck, take care,