Try it yourself. Find a shop that will allow you to take an extended test ride. Not just for five minutes. Or borrow one from a friend. Instead of a "road" bike you may also want to consider something like a cross bike that would allow you to have the flexibility to ride narrow or wider tires as conditions warrant. If I had to have only one bike it would be a cross bike. If you were passed while doing 10-15 MPH it's less likely to be your position on the bike. If you were above that speed you are probably using a lot of power to overcome wind resistance due to your upright position on a hybrid. After the quality of the motor, I find tires make the most difference in performance up to about 16 MPH. Then wind resistance and aerodynamics start to kick in and effort increases exponentially as speed rises. A heavy wheelset will slow acceleration (and also climb slower), but once up to speed their higher inertia will keep you moving. I vary between 250 and 260. Riding 700x25s tires is more than adequate for paved surfaces, including commuting the broken streets of NYC. I can't think of any high performance tires in 35s. If your wheels are a suitable size (including rim WIDTH) try a good tire like a Continental GP4000S in 25. You may be surprised at the change.
One other thing. It's not easy to make the change from a hybrid to an all out racing machine. Torso and arm strength as well as added flexibility are required. For me now 59 years old, in my early 50s it took a couple of years. My bike fit evolved over that time. I still only run a slight drop from my saddle to my bars. Point being FIT is most important. And be aware if you put in the miles that fit is likely to change. There are road bikes marketed as comfort bikes that typically have longer head tubes and less aggressive riding positions.