Android - well i used android for downloads long time back (kitkat) and used apps
for Regular Download - Android Download Manager
for Jdownloader type Downloads - Share Downloader
for Torrents - A-torrent Pro

while Browsing and "None of them Ever Quit"
although i feel there are always some hidden apps that steal your internet-bandwidth(data) in Android.

For Navigation in Android(root) - you can always change the button(bottom three or any other) configration to whatever with Xposed tweak "Gravitybox"

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iOs - Right Now i am Using iPhone which is Jailbroken , then applied a Cydia Tweak called Multiplexor>>Aura. Aura lets any app run in background for infinity. and there is no internet-bandwidth(data) theft in ios(mostly)
so ios+Aura=super strong multitasking


Why download from Mobile Device - well its Really Good to save your Electric Bills

P.s - do you know most of iOs jailbroken tweaks are .Deb files. so i feel its definitely possible for Debian Apps to get installed in iOs, just imagine Easy Debian Ported to ios.