There are pros and cons to both sides of this argument. With the private arrangement, you will first of all need to find your surrogate mother. This is usually much easier done through an agency, as all surrogate mothers to be will have been screened and will have gone through a comprehensive health screening. Also, all of the surrogate mothers with an agency will have had psychological screenings to guarantee the fact that they will be able to deal with the very strong emotions that will be coursing around their bodies during the pregnancy.
Unless, of course, your surrogate mother is a relative or close friend of the family in which case it would seem to be a lot easier. Ethics, moral code and emotions will still loom large in all of the concerned parties worlds. So it would still be wise to involve an attorney and legal contracts so that everyone knows exactly where they stand, and what is expected of them. In most countries and states legal and binding contracts written up by attorneys, are needed by the parents to be anyway. As they are going to have to be legally adopting the child everything, will need to be written clearly and legally about the birth and how it came about. Very often during the pregnancy the doctors and nurses will need to know why there are two women, one pregnant, the other not, and very often two fathers who are so interested in this one child. If you have gone through an agency, they will be able to advise you on what to do and say in this situation.
If you are sorting out surrogacy arrangements privately then yes but if anything unexpected should happen and you are unable to deal with the problems there is a reasonable chance you will end up wishing you had gone to the agency.
Agencies do have trained professionals that can help you with all of the different issues that are involved in surrogacy. From the emotional feeling of all parties, the majority of agencies will have counselors who can help you work your way through any difficult feelings you may have. Also the legal issues, this can be something of a minefield for the parents to be as well as the first time surrogate and all agencies will have attorneys and legal advisers to help you each and every step of the way.
Added to this, there will be requirements held by the intended parents and the surrogate mother, both on what the surrogate mother should be doing while she is pregnant and once the child is born. How much contact the surrogate mother will be allowed to have with the child after the birth, if any, and if any is wanted by the surrogate mother. What the surrogate mother does during her pregnancy. Not just health issues but lifestyle choices as well. Very often these issues when talked about if done just between the intended parents and the surrogate mother, can very often lead to misunderstanding and disagreements. If an agency or an attorney is involved, the third party can very often steer clear of any misunderstandings on their part, emotion is not involved.
Very often, it is advisable, with the high emotions that can rear their very ugly head during this process for the majority of intended parents and surrogate mothers to go through an agency. As with all things though, the decision is ultimately yours and yours alone.