Neither will actually be stronger - they are both serviced by the same access points, which will be configured with both networks. That's not to say your computer might not show one as being stronger, but those strength meters are never all that accurate.

As far as why they have two, your iPhone point pretty much hits the mark. Having "attwifi" means that AT&T cell phones can transparently connect to and use that network, something they aren't going to do to "hhonors". At the same time, having "hhonors" gives Hilton the branding they want.