Interesting question. There is a difference, although a subtle one.
The sun is your ego, your interior individuality, your basic self, your drive, your core.
The moon is emotions, subconscious, your soul, it is what you need to feel emotionally secure, your comfort zone, it works under the surface.
Cancer and pisces are water signs, both emotionally based, very feeling.
Cancer's theme is home, tradition, security, being cardinal it is more goal oriented.
Pisces is etherial, spiritual, creative, compassionate and intuitive, floating in the wind.
So with cancer sun the person would be tied to family and tradition, would tend to be one who accumulates for a sense of security, who is sensitive and closes up within itself when attacked. They would want to build for security, create a fortress. This is their core. Combined with a pisces moon they would be softened, blithely glide through life intuiting, floating through, possibly being over sensitive, using a poetic world, maybe music, to maintain their balance.
Pisces sun would be also a sensitive person, neptunian, hard to pin down, need to live in it's own dimension of the universe.
Cancer moon is nurturing but needs to be nurtured. Ruled by the moon itself, it is moody and changes like the moon's phases, and it can be cranky when it's comfort is disturbed. It uses shyness as a protective shield. So this person would be rooted in the other-world and nebulous, but needing to have its protective shell about it where it can withdraw and hide from what it sees as danger.
The difference is between "I am" and "I feel".
One drives us and gives us a landing pad, the other seeks to suck up what it can from the universe to satisfy an inner need.
So in the case in question, by flipping the signs, one sign sets the priorities and works from the soul while the other works under the innards.
The cancer sun/pisces moon would like to stay at home and listen to soft music.
The pisces sun/cancer moon would go to an evening poetry reading under the stars.
Neither is "better". And a lot will also depend on the rest of the chart, what other energies are hitting these two and stimulating or stifling them. And how we actually see these two persons would depend on their ascendent. Flowing out softly with a fixed but emotional scorpio, or misleading us by seeming aloof with Aquarius that makes us dig deeper?