I think they're both good titles. Considered impartially, I think that the more violent, explosive "Shoot to Kill" would get my attention a little quicker and be slightly more likely to lure in into the theater.

I've never understood why movie titles are changed when released in another country unless, of course, the original title has no meaning in the other language. Is there some legal point to be considered? What would it be?

@GusGorman said:

That is the title of this film outside of North America. Not sure why it was changed but I prefer it over Shoot to Kill.

A great film whatever the title and has a 100% rating on Rotten Tomatoes!

I prefer the title "Deadly Pursuit" too. It describes the movie much better than the original generic one. The title was changed in the UK, because of the Hungerford massacre in 1987.