IPv6 headers are only 20 bytes longer than IPv4 headers, and when you're trying to move a lot of data, like a big download whose performance you care about, you're going to be using full-size 1500+ byte packets (using Ethernet's standard MTU of 1500 as an example here). So the difference is very small. The max TCP/IPv4 throughput of standard (1500 byte MTU) Gigabit Ethernet is about 941 Mbps, whereas the max TCP/IPv6 throughput is about 928 Mbps. So about a 1.4% slowdown.
The other thing to consider is that IPv4 has been around a long time, and many client, server, server load balancer, and router/gateway/firewall implementations may be better optimized for IPv4 in comparison to IPv6. For example, some older routers handle much of the IPv4 work in hardware (sometimes called "fast path") whereas IPv6 has to be handled in software on the router's main CPU, which may be slower. Because you can never know how IPv6-optimized a given path across the public Internet is going to be, or how IPv6-optimized the devices you don't control on the other end of the connection are going to be, it's hard to predict how much IPv6 may affect your performance in real-world usage.
But honestly, I've not found IPv6 to make a major difference in real-world performance. The impact of IPv6 is more often felt when IPv6 connectivity is only halfway implemented on a network, or when a poorly-implemented client doesn't look up DNS A (IPv4) and AAAA (IPv6) records simultaneously, or doesn't try TCP/IPv4 and TCP/IPv6 connections simultaneously. There can be times where a client thinks it should be able to connect via IPv6 and tries that first before timing out and failing over to IPv4, so the real connection doesn't get started as soon as it should. But once a given TCP/IPv6 connection is up, it's competitive with IPv4 for performance.
Edited to add:
I just re-read your question, and realized you were asking about how IPv6 could make things faster. Honestly, all else being equal (which is a big assumption) I wouldn't expect IPv6 to make things faster. However, if your IPv4 connectivity is going through a possibly slow, overloaded NAT (NAPT) gateway because there aren't enough routable IPv4 addresses to go around, and your IPv6 connectivity is being directly routed, then I could see IPv6 being faster. And I wouldn't be surprised if this was the case on a lot of networks.