Ok let's get a few things out of the way right now so people can stop just throwing out random ideas of why you lost.
Stock goodyear 275/60/20 are about 45 pounds each, your M/T are about 64; so you added a total of 76 pounds in rotational mass which is about 300 pounds of weight in your bed.
You make 390/407 and weighs about 5400 pounds(2013 weight from ram) plus you stock. So let's say 5700 plus you due to tires
Your buddy's silverado makes 285/295 if a 4.8 and weighs about 4300 pounds. If he has the 5.3(which I doubt) he makes 295/315 and weighs the same stock plus him
If similar HP you would be 1.4 seconds slower assuming same driver weight, but you have 95-105 more HP
Just for the hell of it, this calculator
1/4 Mile ET Calculator says he would run a 14.9 with 295 hp and 4300 pounds, you would run a 15.0 with 390 hp and 5700 pounds. Mind you that's with only a 17% drivetrain loss, rams lose around 23%.
So using the average 300ish rwhp figure it says you run a 15.5. According to hypertech the 5.3 makes 241 rwhp stock and 257 rwhp with their 93 octane tune. Which means a 15.2 for him stock and a 14.89 with the 93 tune according to the calculator
As comparison the calculator says my 2012 with a curb weight of 5200 should've ran a 15.0 but I ran a 14.6