2018 Trek FX Sport 4 is overall a better bike than 2012 Trek 7300 - it has better components. Compared to 7300 it is closer to a road bike - it has road groupset and it has rigid fork. So, for sure ride will be "noticeably different", you bet! Different, however, doesn't mean faster. Just from the specifications and pictures of these bikes (I don't have first hand experience with these two bikes) Trek FX Sport 4 will probably be marginally faster. Marginally. If you are interested in speed, you need to go to the proper road bike, hybrid with its upright posture and flat bars will not cut it.

But when again, your message is a bit confusing. It seems that though you were riding your current bike for several years, you still didn't get a proper fit on it. Adjust fit on your current bike first, if at all possible (if its size is correct for you). You'll never go fast if your fit is wrong, particularly if your seat is way lower than it should be. Put different tires on it - road slicks. Change to clipless pedals. This will make your current bike go significantly faster and will make it more comfortable to ride.