Couple points.
One, I usually use safari because there is no "set as default" for me to use another browser.
Second, Atomic is my iOS browser of choice. It most certainly has the same behavior as safari. Most apps do but it's the easiest to see in a browser. Some apps work differently like tapatalk. Tapatalk will freeze its UI with "loading" so it can do its thing without UI effecting it's performance. But usually downloading / loading is frozen during UI and if it's constant UI it's frozen indefinitely. Regardless Atomic freezes not by it's choice but by the OS. You know this it's been this way since the start!
NEVER had good luck with downloading anything off the web with any iOS browser. Maybe you can share a link, I always get browser not supported message. Mostly from those file sharing web site, which work fine on even the stock android browser.
Give me a link for want doesn't work for you and I'll try it.
Here's an easy way to test, go here:
http://www.largesound.com/ashborytour/sound/
Hold your finger on the sample MP3 and choose "Download File". You will then see it download in your Downloads menu (third icon from the right on the bottom).