The song "Freakish" from their 1993 album Jelly is an excellent example of their earlier work which was much more emblematic of traditional New Orleans Style music. This tune features brass, reeds, and drums without electronic or amplified instruments. It also utilizes a "Second Line" style groove.
The Dirty Dozen Brass Band is one of the bands credited with the evolution of brass band music to include elements of funk, R&B, and hip hop music. One tune that is a good example of this evolution of the style is "Ain't Nothin' but a Party" from the album Medicated Magic. On this record you can here the driving rhythm guitar over the same "Second Line Groove", which is representative of both styles. I especially like the way that this tune blends the use of amplified instruments with the brass band style of using a basic riff based head with solos throughout the band over one or two different grooves.
Other than the guitar electric organ can also be heard on this track. The Dirty Dozen Brass Band eventually would replace the sousaphone with bass to accommodate changes in personnel. That change moved them into more of the realm a funk or a blues band, but they have retained their brass band roots in both the over arching style of music they perform.