You should consider smaller embroidery and screen printing shops when quality and service matter to you. Larger shops focus on larger clients. They’ll take smaller clients, but they’ll often subcontract the smaller work to smaller embroidery shops. So now you have no idea who is doing your work, and just how much leverage do you have with the large vendor you picked because you wanted to save a nickel per shirt? Not as much as if you choose to do business with a smaller shop.
Smaller shops use much of the same sort of equipment that larger shops do (that’s why the big shops outsource!). They’ll probably do your order in-house in order to make sure it meets their own standards, which are likely to be pretty high because the smaller shops usually want to grow. They’re more likely to be interested in ensuring that each client feels important and is satisfied enough to recommend the shop to others. After all you, the customer, are going to be wearing our work around. Someone will ask you where you had your amazing shirts made. We want you to tell them proudly about the great service you received.