While the skills of the rider are a big factor, even the most skilled rider would have a hard time in competition using a sub-par bike. Don't misunderstand, I'm not saying your bike is sub-par just making the point that the bike and its components play a big role in competition.
With that in mind, any changes you make to your bike should be done with the goal of upgrading the original components which should result in improving the bike's performance. 105 components are middle of the road as far as cost goes but are actually quite dependable and adequate for most riders. The difference in cost between them and the Tiagra group is minimal so I'd certainly opt for the 105 equipment. I've ridden bikes equipped with a Tiagra group as well as the 105, both do an adequate job in most circumstances but the 105s would be a better choice for competition.
In your situation, after upgrading the group, the most important goal in competition would be to reduce the weight of the bike by changing out the wheel set. There's no other component of a bike that can reduce the weight quicker than a change of wheels, after all, other than the frame they're usually the next heaviest part of any bike. Think about changing out the tires also for something lighter. After you make those big changes, you can think about changing out the smaller components like bars, pedals, seats, etc.
The previous answerers made a valid point that changing out components on most bikes is usually not cost effective since you can usually purchase a new bike for less than the cost of what a new group would be. In your case that approach probably wouldn't gain you that much since your bike is an '07 anyway.