In ancient times architects had to use countless geometrical formulae, as well as scientific concepts to complete their projects. In today's world yes there is still math, and science, but lots of it is done via a computer. Also, how often in the modern era has someone built a certifiable wonder of the world? Not as often as our forefathers that is for sure. The men and women in the days of distant summers were artists, they lived to build that which is of beauty. While today, you have many architects simply building in volume.
Yes, because ancient buildings were made to last many centuries and to endure different weather conditions, wars and disasters. Ancient buildings are unique and when you see one you know where it belongs - to which country and to which century. Today, buildings are made by mass production and they are, more or less, similar. Modern buildings are made to last for some time and then to be pulled down and replaced by different one.
I definitely believe that the ancient world had better architects than we have today. They had to be more brilliant, because they had such limited resources to work with. They found a way to build structures that have lasted for thousands of years, and most of our buildings today don't last nearly that long.
I wont say that the architects in the ancient civilizations were better than the ones we have today, this is because the groups operated in different eras with different technologies in place. Ancient architects have build structures that baffles many and so have the modern architects, so they are both outstanding.
There are good architects today, and there were good architects in ancient civilizations. They just worked on different products. Today, builders have many more materials to choose from - steel, glass, for example, that were not available in ancient times. For this reason, the architecture is going to look different. That doesn't make it better, just that it served a different purpose for a different time.