In my experience, furniture is cheaper in Spain. As well you’ll find all kinds of european styles that you probably won’t find in the US. Don’t you think it would be fun to buy your furniture here in Spain instead of back home? It’s part of the adventure of moving here!
From a financial standpoint though, I can’t see how furniture would be so much cheaper in the US than in Spain that it would afford the costs of moving/shipping it from NY to Madrid. It may depend on what kind of furntiture you’re looking for too.
Electronics ARE cheaper in the US right now, mostly due to the valuation of the Euro vs. the US Dollar. The problem you’ll have is buying electrical adapters, which isn’t difficult in itself, just a pain in the ass. Additionally, some devices don’t have their own power converter, in which case you’ll have to buy the adapters with the converter built in (more expensive ($20 or so) and bulky). See Electricity in Spain
About the taxes, generally speaking if your items are packed in a way that they don’t look like new items (in the boxes, sealed, etc), then you may be able to avoid paying customs and VAT/IVA if you can show that the move is permanent. See Moving to Spain: The Move.
Welcome to the Forum by the way, and good luck with your move!