It depends on your budget and philosophy.
I chose to by local so I didn't have to say good Bye local and supported a couple of family run businesses.
I also wanted medium high end appliances and many of the box stores don't carry them. I also think the family run business installers might be higher quality
Many of the higher end appliances are fair trade and the price is the same no matter where you buy - but keep an eye out for specials. I got nice discounts on my elux fridge and Wolf cooktop and oven.

We also bought local. We try to whenever possible. They had the same prices as online and the big box stores. They knew their product and their repair people after being in business a few decades. But we too bought a higher line of appliances after reading so many horror stories about the Whirlpool/GE families of appliances.

I also bought my appliances at a local appliance specialty store. They were very helpful and they matched Sears prices on identical items.