not tried the deluxe bass big muff, but I used to own the std bass big muff. It was a decent enough pedal, but the tall font russian, for me, is so much better sounding. doesn't lose any bass, if anything it adds bass. i'm not interested in the new EHX pedals, not liked what I have tried. i can't see the point of a DI out on a fuzz, and I think if you want options, some of the more boutique builders are a better option (fuzzrocious, wren and cuff, etc). i don't personally go for the obsession with clean blends that a lot of folks have with dirt pedals - the stache and the TFR do not lose any bass, and sound huge.
As for cutting through, I think it depends what sort of band context you use it in. muffs tend to be scooped in the mids - but my fuzzrocious grey stache has a mids control and really cuts through well when you dial this in. The TFR manages just fine, as I use it when the guitar drops out mostly, but would probably struggle in a band with 2 guitarists playing fuzzy guitars into big 4x12's!
I have by no means tried all the muffs out there, but from my experience, the TFR and fuzzrocious grey stache are far better pedals than the std EHX bass big muff, and the deluxe version looks to me like a very big box with a limited range of options. For example, Fuzzrocious offer (in a smaller enclosure) diode clipping, 2nd distortion setting, add a gate, or a tone bypass - far more options than EHX offer.