Switching to touring bicycle: Performance considerations
There are a lot of factors that go into your speed and efficiency, and this switch touches several of them:


Rider Position: Typically, a bike with touring geometry will have a slightly longer wheelbase, and lower bottom bracket. Along with other geometry tweeks, the result is that on a touring bike you are likely to be in a slightly more upright position, increasing your wind resistance.
Weight: As in your example, touring bikes can be 2x heavier or more. This doesn't make as much difference when you are already up to speed and on a flat road. Weight makes a huge difference in acceleration and climbing.
Rotating Mass: Some portion of that additional weight is located in your wider and heavier tires. This increases the rotating mass of your wheels and will also have a negative impact on your acceleration.
Racks, Bags, etc: Having panniers, handlebar bags, and other equipment attached to the bike, in addition to increasing the weight, will act like small parachutes and slow you down.


With all of those factors it's difficult to give you any kind of narrow estimate. I can tell you my experience, switching between riding a carbon-fiber racing bike with a small backpack, and a steel touring bike with one or two panniers attached. I find that over a 13 mile urban commute (relatively flat, but with a large number of potential stops) I am 15-25% slower on the touring bike. For me, much of that is a result of starts and stops (the acceleration effect mentioned above.)