This is a great question. I think we can make a few very important points. First, I would say that through archaeology we are able to see that much of life is the same. This is a remarkable point in studying history. Even though nearly 2000 years separate us from the Romans and those of Pompeii, much remains in common. However, if you want differences, here are three of them.
First, the Roman were much more public. Their day was lived among people and even their homes were for entertaining (the wealthy, of course). We are a much more private society. We can also see this in their public spaces.
Second, the Romans had less technology, even if they were advanced for their day and age. For example, they had to go and get water, whereas we have these benefits. Life was simply harder for them.
Third, the Romans were far more religious. You are able to see temples all over the place. Moreover, these temples were also places of political and social gatherings. In fact, the idea of atheism did not really exist among the Romans. Theirs was not a secular society at all.