Hey Johnny Steele, welcome to the forum 
Keyboard player here as well as beginner as a bass player!
The Darell Freeman video (I follow him on Instagram ) already gives a partial answer: yes, the Little Phatty and Slim Phatty are capable of that sound. On a sidenote, it’s commonly admitted that the Minimoog Model D is kind of a reference when it comes to bass synths. You can listen to Mickael Jackson’s Thriller or to George Clinton’s Parliament or Funkadelic albums to have an idea.
First of all,the Moog sound has its own character and you’ll find it in any Moog monosynth. Now there are some variations in sound as well as in possibilities (number of oscillators, how they can be perfect tuned to each other or more floaty, how you can set them one octave away or more from each other, the filter implementation that differs a bit…). Some of the members here make a big difference between models, others don’t.
My answer is: if you’ve never played any Moog synth before, more than nine times out of ten, you’ll be happy with whatever model you pick as your first one. If not, ensure your purchase can be refunded so that you have a second chance.
Besides sound, there are tow important points: features and interface.
Features: that’s the easy one hehe. You can find them online, compare etc. You said a sequencer could be a good bonus to you. That makes another criterion for you to choose.
Interface is more tricky as it relies on the feeling, the habits you build over the time using an instruments and trying out others. Interface is not only features. Some members will find the Little Phatty’s 4 knobs interface limiting. I remember I thought the same… untill I tried one. And found it very playful. I bought mine few months later. This is very personal as it comes to how you use your instrument, to what you like to do/don’t like to do when playing it (search sounds vs. load presets, play knobs live extensively vs. be happy with only the modulation wheel etc).
I didn’t want this post to get complicated and long, ahem. But I think it’s fair to give you those clues so that you can make a good choice.
My personal experience: I’ve been playing a Little Phatty for years now. When the SubPhatty came out, I was very excited by the one-button-one-function scheme. A friend of mine got one and I still play it once a week to avoid taking mine out. Sound wise, the LP and Sub can get very close. Actually, for the bread and butter, they are equal. Featurewise, there are differences, as well as in terms of interface. On the paper, beside the 2 octave vs 3, the Sub was more appropriate to my usage. But… there is some different feeling that made me decide to keep my LP. Something in the filter overload, something in the oscillators (un)stability, in the way it reacts under my fingers.
Same story when I saw the Sub 37 announcement: overexcited by the feature set, tried it even if I knew the “engine” was the same as the Sub Phatty’s, was not convinced. Maybe I would have got over those little details, maybe not. What I know for sure is that when I search a sound on my LP, or when I just tweak it live to hell, I know where I’m going, I know how to talk to it. Walking in sleepers. I has less surprise potential but all in all I feel it is more suited to my way of playing music with bands.
In few words: it is my instrument.
Hope this helps