I think there are too many variables to clearly say that the hotel does or does not bear a greater responsibility. It would be interesting to hear of the security measures in place.
I know of some Hiltons in Europe whose parking lot is across the street from the hotel and unsecured, and others whose parking lot is totally private and accessable to valets and guests only. My expectation of security is different for those two models. If the lot is wide open and unsecured (even if it's considered the Hilton's private lot), I wouldn't expect anything of the hotel.
But if there was some/any form of security in place, I'd also be considering pursuing something from the hotel. Even more so if you only found out about last week's break-ins by telling them about yours. They should've been warning their guests in light of the situation.