Latency can make a connection seem to be much faster.
As an example, typical HTTP traffic downloads a number of small documents that each fit in just a few packets. Even while typical page sizes have grown significantly, many of the largest parts of pages are often served via cache, where all you need to retrieve is the header confirming the cache is still valid (if even that much). If you download a total of 60K for a page, that's still only a few milliseconds at 30Mbps. A modest latency improvement can absolutely make the same 30Mbps seem to be twice as fast for common activities. This is especially true as web traffic is iterative: the base html document then asks for css or scripts, which ask for more css or scripts, when then ask for resources like images and fonts. So this extra bit of latency delay can be repeated several times to render a page.
Another example is video game traffic. Many games use frequent but very small packets with simple vector or action information about a character or object, where the total throughput is small but the latency is everything. Here, an extra few milliseconds saved in latency can make a world of difference and make the connection seem much faster.
But it probably won't. It's unlikely the latency will be enough different for you to notice this. Additionally, for http traffic server processing time tends to minimize the differences relative to the total page load time from click to rendered. Most important, for larger downloads and things like streaming content, it's the same 30Mbps either way.
There are some other factors that also generally tend to favor the fiber:
- More stability and less environmental interference, meaning less bandwidth lost to TCP retransmits
- The copper line is most likely asymmetric, where your upstream bandwidth is much smaller (not guaranteed, but at this speed asymmetric is far more common). The fiber line is almost certainly 30Mbps in both directions.
- 30Mbps is just what you're paying for today. When the day comes you need more, you can probably turn the fiber all the way up to 1Gpbs with just a phone call to change your billing. The copper is likely to have a much lower ceiling.
- The quality of service on the copper is giving you the max speed, where the average can be much lower. Fiber can generally deliver it's max speed much more consistently.
All of this together means the fiber is definitely the better link. By far. None of this, to me, justifies claiming a factor of 2x for what you have right now, but I sympathize with the engineer in your question, struggling to find a way to explain all of that concisely so managers will understand why it's important.