Joker's right. No pedal can truly match the precision of a keyboard controller. There are some considerations, however. My good buddy plays bass for Siamese, an electronica outfit from Toronto. They let me sit in a few times and I got to use Dave's pedals during a show. He had a Line 6 filter modeler, a Moogerfooger Low-Pass filter, an MF Ring Modulator, an EBS Octabass and an E-H Bass Micro Synth, among others! All of them tracked very well and I had no problems controlling the envelope of the notes. In fact, that setup seemed to be slightly more responsive than a keyboard and you could really control it with the strings. It seems that the bass has a lot to do with this as well. Some basses track better than others.
I've owned a Micro Synth for several years now and it can cover many of the classic sounds. The first time I heard it was at a 2 Skinny J's concert. I didn't know what it was at the time. Their bassist flipped it on and I was transfixed. I just HAD to know what it was. I went up to him after the show and he told me all about it. He had a friend retrofit the vintage internals into a rack-mount unit and oriented the sliders on the front like a graphic EQ! Killer effect.
The ring modulator is a big thing nowadays. Check out Tim Lebfevre. He and Wayne Krantz, the guitarist, use it a lot. Tim seems to have the whole pedal thing worked out pretty well. Some consider him to be at the forefront of pedal-wielding bassists. Other bassists and groups that I've gotten to know over the years are Lake Trout, The New Deal and Siamese. New Deal seems to have changed over into some kind of pop realm now so I can't speak for their recent stuff but their early stuff was good. All of these guys also have their stuff down and you can milk their recordings for ideas and possibilities.
To answer your original question:
In the first video you can clearly see him playing in the upper register of the bass for better tracking. The notes coming out are low so he's obviously using an octaver effect, most likely a synth. The distorted overtones in the middle can be replicated by a synth or a seperate distortion pedal. It sounds like a synth + LPF.
I also love that effect in that second video. The tremelo effect/swirling sound can be created with an oscillator, a ring modulator or other effects. Since the modulator is freq-specific, each note will beat at a different speed. In the video, it sounds fairly consistent so I would guess it's some kind of oscillator or something. If he's using a synth or a Moogerfooger, that capability might already be built into it.
