First of all forget the mechanics as an issue. They are more or less the same functions whether they are for a road, trail ect regardless of how the work is actually done. The shifters might work a little different and the brakes may work differently, but the act of this hand works this brake will be common to all of them. The feel might be a little different, but the actual procedures will be the same. At 11 she is at a perfect age to start and with very little time it will be second nature to her.
Three things to consider. Bikes are like tools. They are designed for a job. The closer you can be to getting the right tool for the job the better. Yes I have used a flat head screw driver on a phillips, but the phillips head driver is far far better. If budget allows I'd consider two bikes. One for trail and one for roads, and I would put the biggest budget on the type of riding she does the most. IF its mostly roads, get the best road bike you can afford and an entry level mountain bike. If its mostly trails reverse. Budget might not allow that now, but if it can with one bike now and another in 6 months its something to consider, but not always the right choice.
The hybrid isn't going to be that much better than a road bike on trails other than the riding position. The hybrids I have seen still use the same road bike gearing and tires. IF you have to have a one bike that does both, this isn't the way I'd go.
A comfort bike will have more of the trail type gearing, and won't be as fast. Depending on your 11 year old size she might be big enough to ride a full size, but let the local bike shop help you. The full size comfort has the hybrid type riding position, but most will have 26 inch wheels that let you put a wide variety of tires on it. Skinny tires for road an fat tires for trail will fit on the same wheel, but changing tires can be a pain. Yet it does work. Id expect this to be just ok on anything but the tame trails, and ok on road.
What I did for a while is take a mountain bike and put narrow tires on the 26 inch wheels. Ok on the roads, but it is in its element on the trails. I bought an extra set of wheels and had street tires on one and trail tires on the other. (can do that with a comfort as well) Even though you didn't need to change tires, there were a few things that had to be done to change wheels mechanically. Not that hard and some 11 year olds could do it, but it might be a bit much for some.
You are far smarter than I was. I didn't ask anyone and had to figure it out myself. grin