Gaston's Hat asked me a couple of questions on a post of mine updating my chase rules a few months ago. Comments made directly on my blog don't seem to be working properly - I can only respond to comments on the G+ share, not ones made on the post directly. I've spent the past month trying to get them to work and can't, so I thought I'd respond in a post proper, and apologise for / explain the delay before doing so.
Gaston's Hat's question:
"In the old version if the fugitives rolled "7" they "have ducked out of sight long enough to hide (either making a Stealth check or Hide in Shadows check) and the pursuers must spot them using their passive perception in order to continue chasing them."
Is a "7" still supposed to allow that?
If that is the case, what if both fugitive and pursuer roll "7"?"
I got rid of Stealth / Hide in Shadows in my games, so no, it doesn't any more for me. I discussed it with a few players after running through it, and it turns out they preferred the option for melee attacks against their pursuers rather than hiding, which could be handled as a consequence of rolling doubles (and thus getting away).
What I might suggest as a possibility, though I haven't play-tested it, is in any round in which the pursuers and fugitives have no matching die results at all (e.g. the pursuers roll 1 and 3, while the fugitives roll 4 and 6), that the fugitives are allowed to make a Hide In Shadows or Stealth check of some sort to try to evade detection.
I think this might make it very easy to get away, depending on how easy it is to access the relevant skill, but that might be intended - it would encourage Stealth-heavy parties to run away, hide, and then either ambush their pursuers or wait for the coast to clear. It would work best for a game where you want a "Metal Gear Solid" feel that prioritises managing detection and escalation in encounters, and where all the PCs have the Stealth skill to some degree.
Anyhow, once again, my apologies for the delay in responding, and I hope this answers your question and gives you a few ideas.