Are there any modern composers that are better than the typical greats (i.e. mozart, beethoven, bach, etc.)?

The reason the "greats" were so great was often because they changed clical music, revolutionized it in some way. Bach is the reason we use the entire system of tonality we currently abide by, Beethoven helped pull us into the romantic genre, and Mozart was one of the greatest geniuses the world has ever seen. No one recently has had that big of an impact--yet. We might not realize the impact until decades later (Bach's music is famous today because Mendelssohn revived it nearly a century after his death). However, Stravinsky and Berlioz were also revolutionaries but are not typically thought of as "the greats." It's really all a matter of opinion. There are tons of 20th century (and a few 21st century) composers who I love. There is bound to be another great around the corner.