When you're looking at switching networks, there are a lot of things to consider. Price, perks, signal range, speed, and so on. You need to make sure you get the best package for your needs, after all. If you're mostly concerned with downloading fast, fast, fast, OpenSignal's latest report might be of interest. It found that EE dominates that category, but in some regions there's some serious competition from Three.
It's its biannual update on the state of the UK's mobile networks, OpenSignal found that on a national level people with EE have access to much higher 4G speeds. Unsurprising, really, seeing as how EE and BT have an insanely large amount of the available mobile spectrum and use it to offer download speeds of up to 300 Mbps. That meant the average speed was 29 Mbps.
The next highest average speed was Three, which was around 6 Mbps slower than EE on average. That's despite it being the smallest of the 'big four' mobile networks. OpenSignal also found that in Three regions (North East, East Midlands, and East of England), Three's average speed was a 'statistical draw' with EE. The numbers weren't exactly the same in these places, but the average download speeds were quite close.
Anyone on Three with the North East will be happy to know that this is the only area where EE was beaten, with Three averaging 30 MBps to EE's 27.9 Mbps
You can see the exact speeds over in OpenSignal's report.
As you can see the general trend was that EE had the best speeds, with Three not far behind, followed by Vodafone and O2. The exceptions obviously being the North East, and London where Vodafone was miles ahead of Three's offering (21.1 Mbps vs 14.5 Mbps).
So if you want the best speeds, you know where to look. That said, you also need to consider availability and signal strength. OpenSignal's September report concluded that EE had the best availability, which makes it that much more appealing for anyone who can find a package that suits them. There aren't any more in depth statistics about it, but in my experience Three doesn't have the best signal - certainly not if you're moving yourself up and down the country.
You can read OpenSignal's full report on the UK's mobile speeds here.