Less than one year?? It actualy depends on the backlog in the local INS office. It can easily take more than one year. And with the end of the REAL ID Act there is no longer a cap on asylee adjustment. So DV application will not be faster than an asylee application.
Moreover, for an DV application you have to provide an affidavit of support (or a job offer), prove that you entered the country legally and have not violated the terms of your stay (unless you are covered by 245(i) in which case you will have to pay an $1,000+ fine to the INS) and you cannot have entered the country using a faked passport or something like that.
And no restrictions about travels? Do not fancy that they will just forget your asylum application because you have adjusted via another legal means. They will always know that you have applied for and been granted asylum. They have your asylum application. They will follow up if you do anything that will cast suspicion on your asylum application.
The only real DV advantage over asylum is that you were married after gaining asylum, your spouse can get her GC with you under DV but not under asylum.