What is the significance of a cross with two cross-bars to Christians? Does it carry different symbolism than a normal cross?
The "double" cross is known as a Patriarchal cross and is well described in the Wikipedia article. There's no point in reproducing more than a sample here:
Incidentally, the figure in the second photograph is Saint Stephen, first King of Hungary: this is his statue in Budapest. He has a halo and is wearing St Stephen's Crown, characterised by its crooked cross. This in itself answers the question!