I think these are reasonably interchangeable. In UK business english i would "chase down a payment from a customer" so here i am adding a little energy to the chase because i want my money! https://www.italki.com/paul_curley

I think the phrasal verb also suggests the chase leads to a point of reaching the target. For example: 1. The police chased the robber. 2. The police chased down the robber. In the first sentence I'm not certain if the police caught the robber but in the second sentence I'm fairly certain they caught up to him.

Chase down is a phrasal verb and means to follow and catch. Whereas chase is just a verb and means to pursue or follow or try to catch.

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