The short answer: Draftboard searches all of your thousands of connections to find paths to your Targets, while the others only search the people who proactively share their networks with you (a tiny subset of your larger network).
And in order to share their networks with you, these competitors have their users ask their connections to either (a) download a CSV of their network from LinkedIn (very clunky process - takes 24 hours to get the CSV) or (b) have them install a chrome extension on their own browsers (most people don't want to do this - privacy, annoyance, no value in it for them, etc).
Draftboard doesn't require your connections to do anything - no download, no upload, nothing.
And that's critical in terms of your ability to find paths to all your prospects: I have 7,000 connections on LinkedIn and each of them has thousands of their own connections - meaning Draftboard has access to literally millions of paths.
In contrast, even if you got 30 of your connections to share their individual networks with you (unlikely), and even if they each have 7,000 connections of their own --> that's only a reach of 28,000 paths. The likelihood that you'll find a significant number of paths to your prospects from that sample size is much, much smaller than with Draftboard.