To be trully considered and answered, this question needs more information. For example, what one religion would everyone believe in? If it is a religion that contains racism and/or allows murder or death , then no, the world would not be in a "better place", but if it is one in which there is actually peace, love, and everyone cared for one another and so on, then yes the world would be better off.

But again this is based off of what one person or majority group would consider better for the world and in the end is subjected to perception, therefore becoming impossible to actually answer because what one person would believe to be a "better world" would be the complete opposite of someone else. In the end, due to human nature to create new ideas and disagree, we would end up where we are now with religion-everyone having their own belief that they are right and others are wrong, thus leading to war, and many other things. In a sense, history would repeat itself with all that is good and all that is bad.

Also, even if everyone believed in one religion it wouldn't neccessarliy fixed all of the other major problems we face in the world today such as famine, illness, death, ect. So the degree in which the world became a "better place" can't be measured and may in fact be only a very small improvment of what we have now if at all. This is why the world would most likely not be a better place if all believed in the same religion.