I see your difficulty.
Your '=IF(H6=I6,"",H6-I6)' formula forces the length of the cell value
to 0 if there is no difference, so by only applying formatting  when
the length is non-zero (ie. TRUE), I can get round it thus:

With ActiveCell.Offset(0, 6)
.FormatConditions.Add _
Type:=xlExpression, _
Formula1:="=LEN(INDIRECT(ADDRESS(ROW(),COLUMN())))"
.FormatConditions(1).Font.ColorIndex = 3
.FormatConditions(1).Interior.ColorIndex = 6
End With
but I see a problem:
Since you want to handle international settings and my solution above
includes a formula as a string expression, this may not carry across
well. I may be having a senior moment, I can't think of an easier way
to refer to the cell in which the conditional  formatting resides other
than INDIRECT(ADDRESS(ROW(),COLUMN())).