I think one benefit of Grad Plus is fixed interest rate. Yes, the rate is great now, but in 5-10 years, what will the rate be? You don't know. I think I remember a financial aid person saying that normally, GP is always a better deal (if the adjustable rate is above 9% or whatever), but right now, private might be, although there is substantially more risk down the line that it won't be and you'll be screwed.
I don't know if there are other benefits to GP, since it's a federal program, that might also weigh in its favor.
Hoping to hear more information from more well-informed people than me...
If you have good credit, DO NOT get the GradPlus. I have really good credit, and my private loans have way lower interest than the fixed 8.5%. Also, there is NO grace period for the GradPlus. Mine technically went into repayment today, as I graduated yesterday. I had to use my one "freebie" financial hardship deferment to avoid paying it over the summer before I start work in October. If I need a financial hardship deferment again (knock on wood), it may be more difficult to get one.
Bottom line, for me, I absolutely 150% regret taking out the GradPlus loan I have. I should've just taken out a private loan my second year like I did for 1L and 3L.