A dual-core coffee lake would be much much faster than a bulldozer at single threaded tasks (like web browsing), and maybe only 20-25% slower at heavily multithreaded tasks. Since you mentioned responsiveness, that's almost entirely a function of single-threaded performance.
In terms of daily usage, the dual-core coffee lake provides a much better experience.
Browsing is single-threaded. 1, 2 or 64 cores will be the same, what's important is how fast that core is.
Have you have used a browser with a dual-core?
Web browsing is heavily multi-threaded.
It's easy to sit on the 16-thread Ryzen 7 5800X and discuss without knowing what the dual-core APUs can