I have iStorage as you likely know. I also have iDownload. The biggest difference is that you can edit documents with iStorage and can e-mail them or upload them. In terms of downloading stuff, most of my experience is with iStorage and it does it pretty well. You can also archive/unarchive zip files with iStorage, organize files within different folders, and search for a particular file (if you have a lot of them). As for opening files, I haven't tried opening any with iDownload, but I have viewed txt files, viewed pdfs, and have listened to mp3s downloaded from the internet using iStorage.
This is one disadvantage of the web browser of iStorage: if you find something on Safari and you want to download something from that URL, you have to write down the whole URL on a piece of paper (since we don't have c/p) and then, when iStorage's browser is open, enter it all at once into the browser address bar. You cannot go back and forth from Safari to iStorage, remembering and entering bits of the URL each time you go back to iStorage. Once you close iStorage, it doesn't remember what you were entering into the address line. You will be directed back to your home page if you close the browser and open it again while in the middle of typing in a long URL. If we had cut and paste, this would be a non-issue.
You may also want to look into Folders, another app that can download stuff from the internet. I have this one too. I forget if this one can edit txt files, but I know it can view them as well as play mp3s. The good thing with this app is that it WILL remember the URL you are in the process of entering even if you close the app.
The winner: I like iStorage, but I do use Folders from time to time. But, you have to remember that none of the apps are perfect at downloading files. There are some files from specific URLs that the web browser may have trouble with (or it may download an empty dummy files). And this is why I own all three app. It pains me that Apple just didn't empower Safari to be able to accomplish downloading files of the internet (just like every other smartphone can).