I've owned both. If you want your bass to sound like lasers, MXR all the way. If you want the juiciest, funkiest low pass filter that can get absolutely wild when combined with other cv options (or even a dirt pedal! I use a TAFM + Subterannea combo and I can't get enough of that tone), the moog is the way to go. I'll admit that I'm partial to moog and ended up selling my MXR years ago but that's only because out of all the phasers, ring mods, flange/chorus and envelope filters out there, the moogerfooger a sound the best and work together amazingly.
That being said, if I could only have one pedal it would be the mf-101 over anything else. It might seem a little big and pricey but it's worth every inch and cent. It's also the cheapest (tied with the ring mod) of the moogerfooger line, for what it's worth. Plugging an expression pedal into the cutoff cv input also lets you use the moog as a wah pedal, if that matters to you. The MXR can't do that. You can also get a nice low subby dub tone if you set the envelope amount to 0. It basically becomes a static filter at that point. If you're gonna shell out for the mxr you might as well spend a few more dollars to get the moog IMO.