Can the an American iPhone 5S work in Europe and vice-versa?

Background

• 
  

  I live in the USA and I have an iPhone 5S (version A1453). It was bought under contract to Sprint and is currently locked.

  
  


• 
  

  My girlfriend lives in the NETHERLANDS and has an iPhone 5S (version A1457). It was bought for full retail price and is unlocked, but currently on the Netherlands' T-Mobile network.

  
  

We are thinking about switching phones, because I have more gigabytes of storage and I don't use that extra space.

Questions

1. 
   

   Will her European iPhone 5S (version A1457) work in the USA (and on which major carriers)?

   
   


2. 
   

   Will my American iPhone 5S (version A1453) work in the NETHERLANDS T-Mobile network?