I my experience (back in the nineties when lost baggage was much more common) - no difference. I wouldn't normally fly first class, mind. But I would fly busine

I my experience (back in the nineties when lost baggage was much more common) - no difference. I wouldn't normally fly first class, mind. But I would fly business now and then, and I was upgraded to first a number of times. I never noticed any difference in how often my case was lost. Big red "Priority" sticker never made any difference. Back then the case was lost so often that I can't give you any number, but it was so often that I got quite used to it. But it definitely made no difference on which class I was flying, or with a gold card or not, etc. Only the airport and other conditions made a difference.