I think it boils down to two schools of thought as far as amplification, basically; rigs that actually produce sound or rigs that just reproduce sound. In an integrated amp the preamp and power amp stages work in concert to produce a sound (probably most obvious with all tube amps), while preamp/power amp configuration generally uses the power amp to reproduce what the preamp outputs with the most minimal tone coloration possible, kind of like a mini PA for the bass. Both are good in my book, but for all out head room and power, the pre/power combo is more practical and/or economical than trying to build a 2000 watt wall of integrated amplifier rigs.
While I have and use pre/power rigs, I prefer to use integrated amps. I think of the entire rig; bass guitar, amp, speakers, cables, effects, etc., as the instrument rather than just the axe itself.
Different integrated amps have specific sounds that cant really be duplicated by modeling. To me modeling sounds canned, and artificial, not big and natural like a traditional integrated amp rig.
Of course, a rig in a box is far more practical from a budget standpoint. Having Ampeg, Reeves, Sunn, Marshall, GK, Hartke, Ashdown, etc. rigs around to capture the specific nuances of their tone is a luxury that few amateur bass players can afford, and unless you are fortunate enough to have roadies are also very cumbersome to gig with. Nothing can duplicate the sound of a full Sunn 2000S rig, or a SVT with a couple of fridges, but dragging around a rig that weighs 300 lbs gets old (and costly) fast. I think a versatile preamp and some sort of modeling effect with a stout power amp and compact speaker cab is far more practical for the average bass player trying to emulate a wide tonal variety of sounds.