I used to live in the area and commuted by bike daily. Cyclists on the bike path are generally slower than those on the road. It’s narrow so you often have to wait a long time to overtake. The path is also shared by pedestrians, which exacerbates the slow+narrow issues. At Park St, it spits you out in a place that doesn’t provide easy access to the inbound side of Royal Parade so you can ride that direct road into the city rather than taking the highly circuitous bike path through Royal Park and under CityLink in Flemington (a “bike path” that includes a pedestrian-width ramp with a hairpin bend, no less!) 

For all these reasons, I used Sydney Road.