Well, they don't take up any space on the Wii, just your SD Card or USB HDD, but nothing on the NAND. Unless you are hard up for space, just keep them. If you want to know more about each app, take a look at their websites, MMM, and Dop-Mii.
Essentially all of Dop-Mii's functions are in MMM, but sometimes Dop-Mii is updated earlier, which comes in handy for example when new IOS revisions are released.
MMM does more stuff. It's a combination of other tools, including Dop-Mii. Dop-Mii is probably more reliable at the things it does, and it gets updated more frequently. Keep 'em both on yer SD card; I do. Just don't bother with the "WeeBrew edition," it's been neutered.
keep MMM for wads, priiloader, ios etc... use Dop-Mii to install any new system updates and channels you need or want; installing system menus with dop-mii will automaticly check if you have the required IOS to run the new System Menu and prompt you to install it.
Dop-Mii v13 is great for Fake Signing, Trucha Bug, Nand Access patc
Dop-Mii Wiibrew Edition is great for installing non patched IOS and new System Menus
MMM is your swiss army knife but i would still keep all 3 i do as i find it necessary to use Dop-Mii v13 when i need certain patches on any IOS
And i use the Wiibrew Edition since can use IOS58+ method which is direct hardware acces
to install any uptodate non patched IOS and System Menus...
Sorry bud, but IOS58 has nothing to do with direct hardware access. It's used for USB 2.0 support, which is unnecessary for...well...any of the tasks here (unless you were installing a LOT of game WADs, yet you're somehow averse to using a cIOS to do it.)
You're thinking of AHBPROT, man.
All of this IOS58/AHBPROT madness started back when TT decided to add support for both in the same rev of HBC; people got the two confused and it's been a mess ever since.
Also, both versions of Dop-Mii do unpatched IOSes just fine.