Congrats on your win! From the little Ive just found on the Breville they both seem to be thermoblock machines which means both will struggle to do a decent job. That said, both will still perform best with unpressurised baskets and freshly, properly ground coffee. Without knowing any more very specific differences that may make a difference, my advice would be to either:
1) sell the 5600 brand new in box and get whatever you can for the Cafe Roma and put the money towards something better and a grinder. Depending where you go, you could pick up a Breville Ikon and a EM0450 for $300-$450 which has the potential to pulverise either machine with preground coffee)
2) if youre happy with what youre getting from the Breville CR, why change?
3) pick the one you like the look of the best
Needless to say, for coffee quality option 1) is the way to go but your priorities may be a bit different to ours! ;)