Do Buddhists believe that by reaching Nirvana that they have come to the same state of mind and body that Siddhartha Guatama obtained?
This depends on the tradition or school of Buddhism. The Theravada school believes that one attains arahanthood which is self perfection under the guidance of the teaching of a Buddha. The Mahayana school considers this a lesser form of perfection and that one should be a Bodhisattva or future Buddha to liberate all sentient beings. Once one becomes a Buddha one has attained the state of perfect enlightenment – the highest goal that one can attain.