Present Perfect vs Preterite

Which sentence is grammatically correct:

- I've been to New York four times, but I've never visited the Empire State Building.
- I went to New York four times, but ....

Can someone explain the difference to me? Thanks in advance!

I think the first sentence sounds a bit more natural, don't see any major problem with the 2nd ("I went to New York four times, but I never visited the Empire State Building.")

What you want to do if possible is to keep it consistent: Preterite & Preterite ; Pres Perfect & Pres Perfect.

It gets a little weird when you mix them as in:

"I went to New York four times, but I have never visited the Empire State Building."

--this is still okay, but it makes it sound as if you are saying two separate/independent statements when in fact you indended to make one continuous one.