I'm planning a visit to New York and I'm wanted to buy a new iPhone 5s unlocked but someone has told me that if I'm going to use it in Spain I might have problems to use LTE. Does anyone know if that's true? It's a problem with the LTE bands used in the US ans in Spain. Or so they say...
Short answer: Get the A1457 model.
You can see the different models and their verified compatibilities here. According to the site, iPhone 5s model A1457 has the support for the LTE bands which are used in most of Europe, while A1453 and A1533 have support for the most common LTE bands in the US. I don't know if the A1457 model is sold that much in the US since it supports only two US-based carriers, but if you can find it, it willl work.