I suppose that some would answer the question in the title to this post, with a question as to why I would even ask the question, since the advantages seem so obvious. But I would submit that the answer is not so obvious as it would seem at first and there may be many circumstances when synchronizing with an online tree is not such a good idea at all.
During the past few years, the idea of exchanging information between a dedicated desktop genealogy program and an online family tree program has taken hold in the genealogical community. There are several local desktop programs that provide the ability to synchronize as a promoted feature of the programs. First, a few definitions.
A local desktop genealogy program is one that operates on your own device, usually a desktop computer or laptop. The idea here is that can keep your own information organized and on your own computer (or other device) without the need for an Internet connection. Unless you export some or all of your data from your program or share a copy of your data file with another user, no one really has access to your information. Sharing data can be done selectively through functions in most programs that provide for a way to export to a GEDCOM file, with the ability to select which individuals or families the user wishes to export. Most of the programs today also provide a method to select a portion of an existing database and save it as a separate file. None of these operations involve online sharing of the information.
Some of the currently available local genealogy programs also provide a way to create an online database or copy of the user's file online, that can then be shared with selected family members for cooperative research. This database or file copy is not publicly available on the Web. In these programs, you can synchronize with the online changes made by other family members.
There a likely hundreds of online programs that provide a website online to build a family tree or upload a GEDCOM file to create a family tree entirely online. These online trees can be public, where anyone who logs into the program can see all of the information in the family tree or private, where only those invited by the creator or administrator of the family tree can see the information. These online family trees can also be created by one particular user or can be a cooperative tree, open to changes from anyone who is interested enough to log onto that particular program. Some online family tree programs provide different levels of access and can be in whole or in part with more than one category of access.
In all of these cases, including the local programs there are provisions for making some of the data confidential, especially that concerning living people.
Now, there are a few programs that promote the idea that you can synchronize data between your online family tree (public or private) and your local database program. Prime examples of these programs are Ancestry.com's Family Tree Maker program and MyHeritage.com's Family Tree Builder program.
In another class entirely, FamilySearch.org has its Family Tree. The main difference being that this is a completely public family tree with universal access. Anyone can enter information into any individual or family on the Family Tree program and all users of the program can edit, delete, add or merge individuals on the tree. There are several programs that advertise access to synchronize data with FamilySearch Family Tree.
The first arguable advantage of having an online family tree at all is the possibility of online collaboration between family members. By putting my family tree online, I can, in effect share what I have done with family members, known and unknown, across the world. In my own experience, this sort of works. Over the years, with a copy of my family tree on Ancestry.com, MyHeritage.com and other programs, I have been contacted by remote family members with some additional information.
But with both Ancestry.com and MyHeritage.com, a new dimension and incentive has been added to the idea of having an online family tree. Both these programs provide automated search capabilities that scour their sources for information about the people on the users' family trees. I see this semi-automatic research as a huge advantage. I have found some extraordinarily useful information by using both of these automated search capabilities. As an added benefit, if I choose to do so, I can install a copy of their local programs on my computer, Family Tree Maker or Family Tree Builder or both, and use the synchronization function to download all of the found sources to my local program. It is up to me to correct any information I have in either program from the sources I find, but the potential to find sources I would otherwise not have found, is tremendous.
It should be noted that in the case of Ancestry.com and MyHeritage.com, although my family trees are shared online, they are my family tree and cannot be changed by any other user.
But now, we have a completely different paradigm. The FamilySearch Family Tree and other similar trees are entirely cooperative. But in the case of the FamilySearch Family Tree, the information in the tree can be easily copied to local programs. Whether or not this process is a good idea or not depends entirely on the sophistication level of the user. Since there is no way to verify the accuracy of most of the entries in FamilySearch Family Tree, the benefit of being able to synchronize information back and forth could be beneficial or very bad depending on the accuracy of the user entering the information. The main check on this information is the ability to add sources for an individual's events. However, very, very few of the existing records in FamilySearch Family Tree yet have sources, so any information contained in the program is unverifiable presently. Ultimately, the information will be self correcting in the sense that individuals participating in the program will add sources and correct the information in the program to be consistent with the sources.
So, in thinking about the concept of synchronization, it is important to ask synchronize with what? If you are merely exchanging information between your own family tree online and your own desktop program, then there is really no risk. But once you add the capability to synchronize data with an open, public and editable family tree online, you had better be ultra careful in choosing what individuals and events you add to your own program on your own computer or device.