Adaptive radiation in the allopatric case would involve organisms reaching disconnected habits, which might be very similar in their characteristics. Probably, phenomena involving small populations and genetic drift (such as founder effects) would help make the differences among species. In contrast, the sympatric case would have to involve species finding different niche in the same place or their evolving very different behaviors, such as nocturnal vs. diurnal activity, to avoid interbreeding preventing speciation.
Work Step by Step
To get to this answer, consider the difference between allopatric and sympatric. In the former case, species could occupy the same habitat in separate places, but the latter case would have to involve mechanisms such as behavior or niche to allow speciation to occur/separate populations to form.