Answer:
Yes, both are good browsers. It is really a personal choice. With IE8 I it is really neglible on which is better. Both perform about the same on many websites. On other sites while firefox might beat IE on one, IE will do better on another.
Mozilla has better connections to some video websites. One of the reasons Firefox does so well is because of the numerous add-ons that are available for it. They range from security, to social networking, to themes. Also Firefox has this thing called "Personas" which can make you feel right at home.
Internet Explorer however has more options prebuilt into its browswer. It can be confusing but a little research can help you figure out what all the settings are for and help for a better browsing experience.