If you can not afford for the system to fail at any time then parallel will most likely be the best bet.

With both systems running at the same time it means that if one fails there is a backup to take over. The new system, which is the one most likely to fail, goes down then the company will not loose any business as the other system will continue to work. This does mean that the employees will be doing double the amount of work. For every order that occurs they need to enter and process it through two systems. This can become very tiresome and very inefficient so it would be highly undesirable to do for too long. It is the safest change over but also requires the most work. This kind of change over is reserved for critical systems such as banks.