The experiences will be totally different. Did you notice that on the tour you "catch sight of" the cathedral? Does the tour allow you actually to do anything in Girona? It's worth a full day: walkable wall; two cathedrals (English audio guides can be rented); beautiful, large historic district; fine museum of reasonable size. But Girona is not on the coast, so you will have no beach time.
I suspect that this is primarily a bus tour to the coast with a rather brief stop in Girona. I am not a beach person, so it would leave me massively frustrated, but your family may love beaches.
You are apparently not using a good website to price out the train tickets. Do not use RailEurope; it may cost you a great deal extra. The Renfe website indicates that if you bought the tickets for September 21 today, you'd have some options at €12.95 or €25 round-trip for each of the adults on one of the fast trains. I don't know your children's ages, so I can't determine their fares. Those fares are even available for the 9:45 AM fast train today (which is just one or two hours in the future as I write this). I don't see any trains with round-trip fares above €25.05, so that looks like the walk-up fare for round-trips. In Spain, round-trips are often about the same price as a single one-way ticket. Remfe can be a bit tricky for US ticket purchasers, so,many folks here recommend using trainline.eu, whose prices will be about the same.
Whether there's a practical way to combine Girona with some time at a beach, using train/bus, I don't know. I hope Enric will see this thread and comment.
