I couldn't eat red meat for about 6 weeks after my gall bladder came out, then I was okay. As I'm mostly a chicken person anyways, I don't eat a lot of beef, and I don't notice that it bothers me when I do--but the fact that I don't eat it often may be why.
I'm confused as to why you can eat a burger, but not minced meat--given that a hamburger is made from minced meat. If you are buying pre-made hamburger patties, then your problem might be the actual beef, not beef in general. As in you can have meat from this type of cow, but not that type of cow.
Ahhhhhh, grass-fed Irish beef. I used to get some minced meat when I was over there that was so lean that you never poured a drop of fat off it and it was so very fine and tasty.
The other difference to be noted is that burgers typically have a higher concentration of fat in them than most (but certainly not all) minced beef. That's because--at least in the US--low fat beef is THE thing to eat. However, you can't make a burger from too lean a beef or it will fall apart. However, the odd thing here is that people with IBS usually respond worse to fat, not better; if you could tolerate minced meat, but not burgers, I'd swear that fat was your problem. However, most people in the US grill their burgers, and this lets a lot of fat drip out; otherwise minced meat is cooked in a skillet and you have to drain the grease out youself, and it's still not as effecient as grilling it out.