First I have to say that giving a small code sample reproducing the problem here would prove very difficult, so I hope that an answer can be given without it 
I have a code fitting TF2 to TH2D. Not standard, for I fit only the position of the function, while the scale is calculated analytically by the function itself for every position. It works in general, but I encountered the following problem. The fitting gives different results (from slightly different to very different) depending on the machine on which I run the code. Exactly same versions of root, but one machine has 32 bit linux, secon 64 bit.
The results are different for Minuit, Minuit2, Fumili2, but same for Fumili (1) and GSL. Not sure if it is bug or feature, but maybe someone can tell me from this short description.