Glad you asked!
Yes there is a difference in the meat and the service. Most times, but not always*, the meat is fresher and of a better quality.
The person owning the Mom & Pop Butcher Shop or small grocery store has a vested interest in the community and needs your loyalty to stay in business. Whereas a chain grocery is an arm of a larger conglomerate and only looking at the bottom line and ignoring quality to achieve this.
In this day and age the large majority of the poultry and meat in supermarkets has been enhanced with a saline solution of up to 20%, which supposedly adds "flavor" but also adds weight and shelf life to the product. You won't find this in your butcher shops. Super stores like Walmart and Target not only have enhanced meat, but also their product is packaged with a whiff of carbon dioxide to keep the meat looking fresher for up to three weeks or more!! Yes, that's true.
Your butcher shop will have knowledgeable personnel behind the counter vs. the large chain supermarket or box store.
* unfortunately there are exceptions and you will need to shop for yourself to see the difference