Either city could keep you occupied for the entire week, so there's not really a mistake to be made here. You'll need to fly between the two cities, so I'd look at skyscanner.com right away to see whether there's a major difference in airfare on April 4 vs. April 5.
The weather will almost certainly be more pleasant in Barcelona, but this may be flower season in the Netherlands. Otherwise, April is not a time I'd choose for that part of Europe, preferring not to risk an encounter with cold, damp weather.
Barcelona has at least six sights for which tickets need to be purchased in advance to avoid very long ticket lines (and possible sell-outs). That makes short trips to the city very challenging. The six sights are: La Sagrada Familia, Parc Guell, Casa Batllo, Casa Mila/La Pedrera, Palau de la Musica Catalana and the Picasso Museum. Except for the Picasso Museum (which is usually absolutely packed so not recommended by me), those are all funky-modernista-architecture sights. I'm not saying that you need to see all of them, or even any of them (though La Sagrada Familia is pretty important), but if you do want to see them, you cannot just wander up when you are in the mood.
I haven't been to Amsterdam in ages, but I think it has been reported on this forum that you need to buy tickets in advance for both the Anne Frank House and the Van Gogh Museum. There may be some other sights where you'd do better to buy in advance. I'd check on those right away, because I don't know how early tickets sell out.
Some travelers have opted to stay in Haarlem, which I think has less expensive hotel rates and is a very short train ride from Amsterdam. I have not done that myself, however.