I haven't really tried carrots with Biggie, unless a piece fell on the floor while cutting one up. He loves the grape tomatoes - but he has to chase them around for a few minutes first. I used to give him grapes, but I was told that they cause kidney problems in dogs. Every once in a while I will give him one though.
My ex gave Biggie some Prime Rib grissle (the fatty stuff) once, which he loved, but Biggie ended up with bloody stool afterwards. We took him to the vet and it turned out he had Ulcerative Colitis which was aggravated by fatty foods. The funny part about this was that my ex had colitis too, so dog and ex were on the same medication.
Now that he's my "ex" I think maybe I should've seen that as a sign. Though I like my dog a WHOLE lot more, so I'd hate to knock Biggie down to ex's level.