The Hilton Liverpool City is crap but does have a lounge and parking is reasonably priced for the location, I would always pick the Doubletree Liverpool over the City Hilton if you want to stat in the City and it is normally cheaper and a lot better with easier access to the tunnel.
The Chester DT is in a nice location, out of the City and convenient for the road from Liverpool although you will be heading with traffic flow rather than against it. I would prefer it as a property to either of the Liverpool options (and you omitted the Hampton which is rarely cheap enough compared to the 2 full service properties, to be worthwhile).
I would go with the DT Chester if you the location works.