I think you might be disappointed with either product if your expectations are high, though I haven't actually tried the '784.
The MFJ-1026 works for what it's good at, but it's a bit technical to get it to work right, and by the time you get it to work *well* you often might as well have fixed the problem at its source.
But it can do two things... it can null out a noise in your own house pretty easily... you just need to put up a noise antenna that hears the noise signal very well without hearing your desired signal much and you can make that noise vanish. It's almost like magic... tricky to adjust magic, but magic.
Unfortunately, the "right" noise antenna for me has always been different on every band, and the noises come and go and change relative phase enough that I very rarely find it worth using the canceller. For a while I had some awful noise on 20m and 17m from a neighbor's electronic device of some sort, and it was nice that I could get rid of that when I was pointed south or southwest where it was bad.
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But here's the problem... if you get more than a few wavelengths away from the source, you're often going to need a very similar antenna to your main one to give you your noise signal... and that means you're going to end up a real phased array. You can successfully null out directions this way, your Mexican industrial park noise might go away, but you're basically going to have a NULL in that direction for ALL SIGNALS ...
Maybe that's OK for you, but it killed the utility of the device for me here. When I tried to use my MFJ-1026 for the reason I bought it, which was nulling out the noise from some elevators on 80m in an apartment building northeast of here, I succeeded but would also null out the desired European and Middle East stations!
You can use different polarizations to alleviate this somewhat, but when I tried to use a horizontally polarized noise antenna, it barely picked up the elevators and it *strongly* picked up some power line noise... so I could not really null the elevators with it, and even if I had, the power line noise would be mixed in.
So all in all, the MFJ noise canceller actually works but it works in a way that makes it seem like it doesn't work to many folks who try it out. It might cancel some of your house noises, but so would ferrite cores on all the electrical cords, which is a more direct and easier solution, probably.
As far as DSP goes, you might try it, but it'll probably just make the noise more pleasant to listen to, not really get rid of it (noise is a signal, after all), and I have to wonder if your digital decoding software would care one bit... I'm not sure it would.
My audio DSP in my FT-857D isn't the greatest in the world, I'm sure, but it blunts the edges of some noises enough to make it worth turning on the digital noise reduction... but it doesn't make a bit of difference on copying PSK... in fact, if anything, it makes copy worse but I haven't been able to test that rigorously.
73,
Dan