I prefer Yachtsman over Bistro de Paris, but look at both of the menus online and see which looks better overall to you (individual dishes might change over time).
Service: I've had some great service at Yachtsman, and very good service at Bistro. The thing with Bistro is that my meal took over 2 hours (I was dining solo and not showing any signs of wanting to linger). So my Bistro meal progressed at a snail's pace, whereas I'd say Yachtsman is usually just right.
Ambiance: Lots of families go to Yachtsman, and it can sometimes get noisy (depending on where you're seated). However, to my surprise, Bistro de Paris was also full of families and even louder than Yachtsman (the noise factor will probably get worse now that the
DDP is accepted). Also, the tables at Bistro were extremely close together, and I could hear everything my neighbors were saying. While I think Bistro has the potential to have a nice, relaxing, upscale ambiance, I prefer Yachtsman for the classic steakhouse feel and the fact that tables seem to be more spread out.
Food: Most people go to Yachtsman for the steak, a simple but well-prepared protein with some potatoes on the side. We like Yachtsman because some of its appetizers, desserts, and entrees are quite creative. In fact, I'd say the steaks have almost always been the least spectacular part of our meals here (even though they're quite good). At Bistro, expect some beautiful presentations but more classic French flavors (aka not always innovative). My food at Bistro was good, but the taste didn't really wow me.