"J'ai beaucoup de temps" is rather neutral in terms of meaning. It just mean that you are not in a hurry.
Often "J'ai tout mon temps" is different because it is something you would say almost as a threat. Since I have all the time in the world, I'll wait for you (a disobedient child) to do whatever as long as necessary.
Sometimes, it is said to mean just the contrary: you are in a hurry and your counterpart is really too slow.