When testing a web site, I tried to grab as many different browsers and devices as possible. And that's where I found Puffin. In a word,
Our web site was operating behind a separate firewall but even then, Puffin delivered pages at least 2-5x faster than Chrome or Safari and this was on an iPhone 5C. Even on an iPad 2, Puffin's speed is incredible.
It also supports Flash if you need it. Maybe more so - it's download mechanism is powerful too. On your phone, the chances that you are downloading something directly to your phone for use on your phone is unlikely. Instead, you likely want to refer to it later. Puffin has cloud-to-cloud drive support so when you want to download a file, it will send the link to your cloud drive (like Dropbox) and download it behind the scenes there. The result? Instant download.
It works for both Android and iOS. There is a free version but the full value of the Download is found in the Pro version (all of 0.99$ in the App store).