Well, you didn't specify how eating would kill you, and it won't do it by itself, so chances are that you'd live longer, though it would be debatable if that's a good thing or not. If you've never seen an animal gorge itself, you might not think over eating is a big deal, but it can be agonizing under the right circumstances. Draw that out over time with the inevitable vomiting occurs between bouts of stuffing yourself, and you're slowly losing any ability to digest things right, and the months you would last could be hell.
Starvation is pretty unpleasant in itself, though. Even fasting for short spans can be painful and stressful beyond the hunger itself. The hunger goes away after a while. Starving to death can take weeks.
Seriously, even people with Prader-Willi can't stuff themselves so full as to die only from eating. It's long term issues that give them trouble.
But being forced to constantly eat, while your body ends up vomiting from it, only to have to go at it again, that's pretty horrible.
You'd have your teeth eroding faster from the constant use and effects of acids. The mucus production in your digestive tract couldn't keep up, which ain't going to be fun. The constant pressure in the belly is painful too. I'm really not sure his long a person would last with everythinggoing on, but people have survived years binging and purging.