I tried to shop Jet (before they were acquired) and I found the search / shop experience had too much friction. Amazon's UI has plenty of annoyances, but they've made it _real_ easy to get something into your cart and check out.
On the other hand, all of my music studio purchases I make at Sweetwater. Great customer service, free shipping, will price match if you ask, and frictionless returns.
IMO Amazon is vulnerable to good competitors, but the emphasis is on good. I can tolerate a small shipping fee, and I don't need next day or two day shipping (although it's nice). On the other hand if you make it hard for me to shop, customer service sucks, or I have to jump through hoops to return something, I'll go back to Amazon.