The labor of predicting LIBOR....

Should I choose a private student loan based on the 1-month LIBOR or the Prime Rate? I have private education loan approvals that are based on both the 1-month LIBOR rate (more specifically, the quarterly average of the 1-month LIBOR) and the Prime Rate. Chase Education is calculating the 1-month LIBOR currently at 3.62 (an average of Jan-Mar rates of 4.223, 2.849, 2.708) and the April rate has posted at 2.486, so a clear downward trend. Historically the lowest LIBOR has hit was 1.340 in 2003. My margin with Chase would be +2.5% so right now calculated at 6.12%. The best offer I was received based on the Prime Rate is Prime +1%, so right now a rate of 6.25% with the margin. Within the last ten years, the lowest prime rate was 4.0%. Both rates have obviously experienced cuts in the past quarter, but other than a crystal ball, is there is any way to get an idea of which rate will experience further decreases and thus save me from accruing more interest?