Differences

Rhythm:

•        More syncopation in Muddy Waters example (makes sense as the Chicago blues style has more jazz elements such as syncopation than traditional Delta blues).
•       Drums carry rhythm differently, bodhran in Julie Fowlis example has a totally different style of being played

Tonal Elements:

•       While Julie Fowlis example very clearly has a major tonality despite microtones used in the vocal part (perhaps due to it being a folk song, it has a clear major tonality that is always relative to it’s tonic), the Muddy Waters example while major as well uses mainly seventh chords and can be a dissonant at times (again due to the nature of the blues style).