Most of us who use Outlook with Palm don’t spend time in the Palm DT application, so there may not be many folks who can provide comparisons. To answer your questions about Outlook through Outlook 2003:
There’s no split screen – there are a variety of Views, under View | Arrange By | Current, but they are either card views or table views. Customizing the Views to something like the Palm DT is way beyond the Forms customizations Outlook provides; it might be possible, but it would be an enormous effort.
There’s no “progressive” Search entry field, not in the Find Window, nor in the Advanced Find window (Ctrl-Shift-F).
You’ll have to get used to the way Outlook works (and doesn’t) – even those of us who are experienced users find plenty of annoyances. But in my brief looks some time ago at Palm DT, I think Outlook captures more data – perhaps not.