There are a number of ways that you could define each country's viewpoints regarding this war. I will set out how I see each viewpoint.
For the US, the viewpoint was that the Spanish were brutally subjugating the people of Cuba. Many Americans felt that the Spanish tactics against the Cuban rebels were atrocious. They also felt sympathy with the Cuban rebels since they were fighting for independence.
For Spain, the viewpoint was that Cuba was an integral part of their territory and they were trying their best to accomodate the rebels' demands. They felt that they were trying to improve their rule of Cuba giving the island, for example, some amount of autonomy.
As to which is more convincing, I would say neither. Americans did not really care about Cuba's independence, as can be seen from the fact that the US took a great deal of control over Cuba after the war (see Platt Amendment link below). At the same time, the Spanish were only really trying to give Cuba enough concessions to get the US off their backs. They were not really sincere about relaxing their hold on the island.
I would argue that this was a plain and simple war for territory between two imperialist powers and neither side's arguments were very convincing to me.