So, after playing around with it... I still think that there is a place for both together. Each day, you get points and accumulate a streak. Your point totals for each day is compared with your prior point total. When the streak is broken, your points for the entire streak are tallied for a point total for that streak. So in the end, you get more gamification by the fact that your streaks and point totals for the streaks and days are compared.
Also, I think that adding the ability to set certain goals and rewards for those goals would be a useful addition.