Blue99 has given you a very good answer. Essentially the difference between a 0w30 and 10w30 is the base oil and Viscosity Index Improvers (VII) used. Yes, the 0w30 starts out thinner, and depends more on the VII to hold up at higher temperatures, than the 10w30 does. And VII break down over time (poorer oils faster). But this does not mean you should use a 10w30, unless you are possessed with extended oil change intervals. You can do your engine a favour by using a wide range multigrade (high VI) and change the oil on time before the VII breaks down.
There is one more variable to consider and that is the group of the base oil. Lower grade base oils can have a VI in the range of 100. A wide range multigrade needs a VI in the 170 range. This will take a lot of VII and will make an oil more susceptable to viscosity breakdown. The other choice is to use a high grade synthetic. Good Group III's and IV's are around 130 with no VII. However, contrary to what some may think they still need VII to reach the required 170 range (unless you're Redline and see nothing wrong with producing oils closer to 150). So this is one advantage of synthetics. They can have a wider multiviscosity range and still hold the high temperature viscosity better as they age because they have less VII.
