Comparison of results with Direct form1 and Direct form2 implementation of IIR filters
Will the Outputs of both implementations be the same, always (i.e. error is almost 0)?


That depends A LOT on the numerical precision of your data representation and mathematical operations and on the filter itself, specifically the location of the poles. 

If you use double precision in a communication application, there should be little to no difference. If you are trying to do audio processing with 16-bit fixed point format, the errors induced by Direct Form II are so large that it's basically unusable.