I think there are lots of different ways to do this and much of the time, it's not low emotional intelligence or rude.
If you are telling a story about how you felt totally ridiculous when xxx happened to you, it is totally fine to respond with "ah don't feel bad, same thing happened to me"
If you are seeking advice on how to deal with something "when it happened to me, I tried xxx but preferred yyy, have you considered..?" Is totally fine
If you are talking about how something made you feel, it can be totally fine to talk about your feelings in response to show empathy etc
Obviously what's not fine is just to interrupt and make it all about your experience.
Or responding in a superior way - I have one friend whose response any time I have even the most gentle whinge about parenting is to say that her experience was the total opposite because her daughter never ever had a tantrum/put a foot wrong/is totally perfect
I like a conversation to be back and forth not just monologues in turn and the way that often unfolds is swapping similar experiences