I'm still not sure why one time traveler would want to destroy another. There has to be some other motive than pure power.
I think Ben is interfering with Widmore’s efforts. Blocking him. Or perhaps there can be only one truly or fully functional vortex or loci on the planet at one time. Or Ben has the more powerful device powered by the larger amount of anti-matter and Widmore can never get control of it without capturing Ben.