It all depends on which brand you feel more comfortable with. The Cadillac Northstar had some issues with the head gaskets, and head bolts stretching. In '03 they were very good and all those bugs were not found anymore. Some issues with air ride also could pop up. This also goes with any electrical gremlins to look out for. Meaning the switches and such. The 4T80E transmission is very durable, some claim to have issues, but maintenance is key with luxury cars.
Lincoln's InTech was a very durable engine, it was the same engine placed in the SVT Mustang Cobra. 95-02 Continentals have the TekSid block which was forged in Italy during those times. It is very durable, all aluminum block, aluminum heads, aluminum intake. For '99 the Continental had received the C heads, which were improved for increase air flow resulting in more power, power went up from 260 hp to 275 hp. The issue with Continentals are the AX4N transmission, they some what overheat because of it being mated to a performance V8. The Torque converter clutch and clutch packs tend to have increase wear. Trans fluid replacement should be every 15K miles for maintenance. Check how the transmission shifts, the transmission model can be either an AX4N, 4F50N, AX4S depending on who owned the car at the time of the rebuild or replacement. If the dealer had replaced it I believe it to be a 4F50N tag on it. Air ride can be some what problematic like any luxury car brand.
This is all I can think off hand for now. LVC is full of info, on issues that are known. Others will chime in.
I hope I helped you. Good Luck with your car purchase!!
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