I am looking to buy a DX-398 and was wondering if this unit has better
reception than an ATS-505? I listen most to MW, but I wanted to get into
some SWL. I am new to swl.

The DX398 and the Grundig YB400 will both out-perform your ATS505 admirably.
The '505 is not a bad radio (used by many people, and does what it does
satisfactorily) but it doesn't have the same 'oomph' as the above-mentioned
radios. As for having 'better reception', in almost every case you'll find the
features on the 398 to be more friendly and helpful in pulling out weaker
signals than the 505, and while a good strong signal in your location may not
seem any better on either radio, the difference is in weaker signal ability,
and on that account the 505 cannot pretend to perform as well as the 398.
You should be able to find a perfectly satisfying unit of either radio (and
there are others as well) online at auction sites, used or discounted at
radio/electronics suppliers, and so on.
I have a feeling that if you've been using the 505, and then step up to the
398, the YB400, the Sony 7600G, or other portable, it's going to feel like
you're hearing SW for the first time. And in the case of weaker signals and
signals being pulled from noise or interference, you will literally be hearing
them for the first time.
Best of luck, enjoy the hobby!
Linus