I presume Spanish slate is very similar to Welsh slate in looks? Probably a daft question as I can't help picturing those red terracotta type tiles when thinking about Spanish roofing material, but they are not slates.
Anyway, I think your neighbour is nuts to go for a different material to yours, as you say they will be different sizes and there will be a join down the middle. It will look horrible IMHO. When I moved into the house I'm in now, which is also semi-detached, I changed the cladding to match my neighbour's (it needed changing anyway). The result was that both houses look bigger and better. They are not broken up by dark wood cladding on one side and white PVC on the other. Why don't you both pay to have the roof cleaned and tiles replaced if and when necessary? It will be much cheaper, especially for your neighbour.