Unless you get specific advice to this effect, I would not assume you’ll get a quicker response with a direct app. For most schools, unless there is rolling admission, everyone in a given round of admission (EA,RD, etc.) finds out at the same time. I know there are some exceptions to that rule, but not many (offhand, I can think of William & Mary for those who get the Cypher post card, McGill’s gradual admissions release, which has little to do with when you apply, and some – but not all – honors admissions for CU Boulder). For the most part, the difference in the notification date is which application round you choose, not which app you use or how far in advance you apply. And using the schools’ apps might backfire in the sense that it’s a lot easier for your kids’ school if they have to upload letters of rec, transcripts, and other forms to fewer platforms. When you use a lot of different apps, they have to negotiate far more systems, and it could take longer.
So be sure you absolutely know there is an advantage to a direct app before you decide to go that route. I really don’t think there are too many schools where this is the case. Even if the common app is not a perfect match for the individual schools’ apps, I don’t see how the schools can show preference for their own version when common app/coalition use is so universal. Otherwise, just be sure you apply by the deadline you need to so you can maximize chances of aid: as early as possible for rolling, EA by the deadline where available, and RD everywhere else, assuming you’re not doing ED (with a fixed EA or RD deadline, earlier doesn’t matter as long as you get the app in on time).