The first riff is what I call my "groove riff". Now this is not your typical groove riff because we don't have much rhythmic variation. In this case, we have a tremelo picked riff that has an underlying half-time double kick part. The half-time feel in the drums gives it that groove feel.
Theoretically these riffs are all interchangable and the main factor that affects the feel of a riff is the drum part. For example, if you wanted, you could play blast beats over the entire first riff and it would no longer be considered "groovy". The whole point I'm trying to make is to have variation within your composition.
You may notice that there are not many notes to this riff. We'll want to concentrate more on the right hand technique in the riff.
One exersice you might use to get your right hand tremelo speed up to par is to play accented sixteenth notes along with metronome.
1 e & a 2 e & a 3 e & a 4 e & a
Making sure to accent on 1, 2, 3, and 4 will help to develop more speed while tremelo picking (drummers use the same technique when developing speed).