Its depend on the situation. If a student is disable so for that home exams are better for which different universities are present. Regarding reliability its depends on the course and class. If a student is preparing a research paper so either it home are at class same. But to guide the student classrooms exams are also reliable and important. And also its depend on the study level a research level study want that you have to know and do so either at home or in the class. But both type are the requirement of the day.
I dont think both are reliable, because with sit-in exams, student just do rote learning just to pass and discard everything away, and with take home exams, students just copy from sources and submit without understanding what they are copying.
I tried a take home exam, for college students, once in the late 1980s "no internet at that time" and decided, afterwards, to never repeat it again. The exam included 3 "tough" questions so most of the students went to consult some school teachers who I know !! I saw from the students papers that the school teachers tried hard but they failed to give final correct answers.
In my opinion, sit down written exams are relatively reliable but the most reliable are the oral exams. This way, there will be no chance for cheating.
More reliable in terms of what? If we want to measure supervised real time performance (despite its many shortcomings) classroom exam would be reliable. But if exams are to be done in relaxed manner and with ample time to think and plan home take could be preferable. This is provided that cheating is assumed to have been controlled in both cases.