Difference between 新式 and 新型
I believe they are almost interchangeable.


  新型建筑 新式建筑 
  
  新型计算机 新式计算机
  
  新型设计 新式设计
  
  新型武器 新式武器
  
  新型手机 新式手机




A little concern is that 新型 is primarily for things that does have a 型/型号.

For example， most digital devices and most industrial products always have 型/型号. So 新型 and 新式 are both good for them.

On the other side, most art-related products have only aesthetic concerns and have no specific 型/型号. 新式 could be better here.


  新式服装 新型服装？
  
  新式婚礼 新型婚礼？
  
  新式歌曲 新型歌曲？
  
  新式糕点 新型糕点？
  
  新式化妆 新型化妆？


Still, I re-point out that, to a native speaker like me, they are almost the same and interchangeable.