As a general rule, a big law firm does a lot of business/commercial law, which I would guess is because that kind of law often requires a lot of manpower. On the other hand, divorce law is more typically practiced in small and solo law firms.
The large commercial law firms may have a few family law attorney on staff so they can provide those services to the firm’s clients, but in my experience the most well known and respected family law attorneys are in small offices that do not do much besides family law. I suppose that is because they want to have more control over their own practices and not answer to a large firm management structure.
One thing I would recommend looking at when hiring a divorce attorney is whether family law is the primary focus of their practice, or just one of several areas they practice in. I would not expect an attorney who practices in several areas of the law to know as much about any of them as the attorney who focuses on the one area.
Ultimately it is not the size of the firm, it is the quality of the service you receive. This means the attorney should be very knowledgeable about divorce law. The attorney and the staff should be responsive, returning calls and emails within a reasonable time. The attorney should listen to you, your goals and concerns, and not just talk about what they plan to do. The attorney should be as skilled at negotiation as they are at arguing in court. The attorney should be good at advising the client, discussing the positives as well as the negatives of the client’s case and giving a realistic picture of the potential outcomes. The attorney should be able to work with the opposing counsel to come to agreements when possible rather than treating every case as open warfare.
Many family law attorneys do not even work downtown. If you need a divorce attorney, there may well be some very skilled people in your own neighborhood!