First let's define the terms. A general practitioner is an attorney who does several different area of law. For example, s/he does 20% Family Law, 30% property, 20% criminal, 25% civil litigation & 5% landlord/tenant. An attorney who concentrates in an area of law will do that area of law roughly 2/3 of the time (or more).
I'm a firm believer in the adage "a jack of all trades is a master of none." Another good analogy is in medicine - if you had a heart problem, would you want to see just a general practitioner or would you want to see a specialist? I'm guessing most people would want to see a specialist. Same thing in the law.
I'll give you an example from a recent potential client I serviced. She went first to a general practitioner, who told her she would not qualify for maintenance (i.e., alimony) if she was not a housewife. That statement is so far from the truth as to be outright deceiving. While certainly not all non-monied spouses will qualify for maintenance, New York has a maintenance calculator which gives one the presumptive amount one is entitled to: http://www.courts.state.ny.us/divorce/calculator.pdf.
Next, this same general practitioner advised the potential client to handle her child support & child custody issues in Family Court first before filing for divorce. The problem? The parties still reside together - if she had attempted to file either such petition in Family Court, the Judge most likely (certainly not definitely) would have dismissed the petitions given that they still live together.
In sum, as a general rule, it's better to go to a specialist - whether one is dealing with the medical field or the legal one.
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Divorce / Separation Lawyer