Pure math field for PhD when planning to go into industry
It's hard to say much without more concrete info about which fields you are talking about. 

I switched from geometric analysis as academic to quantitative finance in industry pretty easily. But it was probably easier at the time in that they didn't expect you to know much, just be smart. 

Being an analyst meant that the distance to applications was much shorter than from many fields. However, the PhD badge does help whatever your original field; I have helped people with topology PhDs make the switch. 

My general advice to people planning to switch is to do something related to probability or statistics. There are plenty of pure problems but it leaves you well placed for applications. 

(see my guide on www.markjoshi.com for more discussion.)