The tests are VERY similar. I took both, but it was a few years ago. The tests may have changed by now. When I took them, each test was about 4 hours long. A verbal section, a math section, and two essays (each you get like 30 or 45 min). You get one 10 minute break between the essays and the verbal & math section. There is a RUNNING CLOCK during your 10minute break, so make sure you run to the bathroom, grab a snack and some water all within those 10 minutes, or the test will start back up without you! I recommend bring your snack/water with you. They make you put your keys, wallet, cell phone, and anything else you have on you in a locker and they give you a key before you enter the test. I didn't notice much difference in the tests. The GMAT is usually required for MBA programs, and the GRE is required for other graduate programs. I noticed the GMAT didn't test your vocbulary like the GRE did. By that I mean that the GRE would have questions that give you just a word, and you have to pick the word that is the synonym or antonym. Those questions weren't on the GMAT when I took it. The verbal section of the GMAT was more reading comprehension and picking the best word of phrase for sentence completion. The GRE also had a few "dummy" math and verbal sections, where I had to answer the questions but they had no impact on my score. However, I didn't know that these were dummy sections, so you should do your best on all questions in the test.
Word of advice on the essays, I got over 5 out of a possible score of 6 on both test ( a 5 and a 5.5), and can honestly say that you don't need to have a big sophisticated vocabulary to get a high score. You just need coherence. Make sure your essays flow in a logical and are literate.