If you are interested in the theory, the answer is yes, there is a change. If you are interested in dieting, the answer is still yes, but it is quite irrelevant to you.
There are two types of browning reactions, Maillard and caramelization. Both start with highly complicated molecules and end with different kinds of highly complicated molecules. For a very precise answer to your question, one would have to know every possible chemical reaction occuring there, the energy trapped in the precursors and in the resulting molecules, and whether this energy is accessible for the human body (e.g. there is quite a lot of energy in raw petrol, but your body can't extract it if you happen to eat it). As these reactions haven't been studied in this level of detail, it isn't possible to give you a really precise answer.
On the other hand, the tendency would be for the calories (at least the digestible ones) to fall somewhat. First, the calories from amino acids and carbohydrates (which are the inputs for browning) are digestible; some of the reaction products can be digestible, but not all will be. Second, some of the calories will literally disappear in thin air - because some of the products of these reactions are volatile.
But if you are expecting to reduce your dietary calorie intake by eating toasted bread, it will probably make no difference at all. First, the calorie-reducing effects will only occur for a small part of the molecules involved. Second, and more important: even if it did occur for all molecules involved, browning only happens on the surface (theoretically, it could happen on the inside too, if you heated it in the 154°C - 190°C range. Practically, if you are doing that, nobody will want to eat that food). The surface is quite small as opposed to the rest - let's assume a slice with 1 cm thickness and a generous browning of 0.5 milimeter depth. (I know that the part which gets hard is thicker, but it doesn't really get browner). I'll disregard the surface enlargment caused by leavened-bubbles in the crumb (because I'm afraid I might end up with an infinite fractal surface :) ) and then we have ~10% of the slice browned. As I said, there is no chance that all the calories in this part disappear completely, and I doubt that the reduction will be really significant. But even if it was at really high 50%, you only get 5% reduction in total, or 10 calories per slice of white bread, less for diet-friendly breads (and this number is just an inflated best-case guess).