Here we go again, heading down the "Great Divide." First, the Intrigue, when outfitted in a nice color and with nice but not too garish accessories, is a truly beautiful vehicle.
I suggest the 3800 V6....emphatically. This would only limit you to the 1998 model and the first portion of the 1999 model year.
I have rented a handful of each of these. In ordinary driving, you don't notice the difference. The 3.5 seems to be better in the mid-range pass...stomp on the pedal and you will feel some pushback into the seat. Again, I beg to differ...the 3.5 is smoother, but not by leaps and bounds. The 3800 is hushed enough in this vehicle.
Neither, in this range of model years, is totally trouble free. The 3800, in Series II form, may have intake manifold problems.
However, problems encountered with a 3.5 will be more expensive as the engine itself is newer and more complicated. The reason why I assert this belief stems from only one experience....but it was an eye-opener.
I had a neighbor (an elderly woman) in a Sacramento suburb that had a silver 1999 Intrigue I would salivate over. I spoke to her every once in a while about her car. I finally told her if she wanted to get rid of it or trade it in, to come to me first. She beamed and even added "and it's got a new engine...the dealership replaced the first one under warranty." At this point, I demurely asked if I could lift the hood. Staring back at me was a 3.5 litre V6. An engine blowing up in a NEW car is INEXCUSABLE. I don't know of ANY 3800s that have gone kaput under the warranty period....nor within the first 150,000 miles of operation for that matter.
Good luckand let us know what you decide to do!