They'll fit in the cages, so you can throw your bottles away and use the ones they give you. The only problem is that they tend to crush a little, and don't fit so great after you start drinking sometimes. What I do, though, is pull the whole top off the bottle and dump it into my water bottle while riding. You have to be pretty comfortable riding with no hands to do that, though. If you're not concerned about time, the best thing might be to pull over and refill. It'll only end up costing you maybe two minutes overall with all the refills.

If you have areobars then you can use an areo bottle(fits between the areobars) - those can easily be refilled on the fly - no caps to open - just dump it in.
You should also see how the gatorade bottles fit in your cages. I don't have any issue. Then start the race with those - then you aren't tossing one of your water bottles at the exchange or having to stop to refill.