If it were me I'd be going for the Jag. The missus has 2 litre X-type, and to be fair not a bad old car, not as quiet as the LS, seats a bit narrower, but for a small engine can pull fairly well even with four people in. Fuel economy is good for such a big car. Sound system nowhere near as good, but some models come with Bluetooth, which would be nice to have in the 400.
Interior is different, but no worse/better than LS IMHO.
Just check the openings under the door sills for rust, some are really bad and some seem to be perfectly okay. I found ones later than 2004/2005 to be best to go for, and good value (but not as good value as LS).
I found the S-types too cramped for my liking, and having driven the Aero, a nice car, but thirsty and also felt cramped, and the dashboard/console felt way too clumsy to me.
Never driven a GS300, but been in one or two, and they seem to be okay, but the boot space was not to my liking, though I think they look a bit nicer with the bodywork styling.
Whatever you end up with, hopefully no one will be trying to park in the back of it.