I think both are really good and I think they both have absolutely top quality meat. In my opinion both will serve you well but I think the key distinction is:
Chosun is a nicer place and if you let them know that this is a special ocaccion then they may be kind enough to set you up with one of the better servers. When trying to impress those two things do make a difference, Korean or no.
Park's has a charcoal grill and that makes for the better food. In fact, I'm of the belief that the meat quality is the same but it's all in the grill. It's sort of Chosun (top quality meat and a working ventilation system) meets Soot Bul Jeep (most soulful expression of the grill).
If the best food possible is the goal then I think Park's is the choice. If service and high-end atmosphere is very important then Chosun. Both are fairly pricey.
Park's has meat with much more flavor than anything chosun can offer. the price is similar; they are both on the higher end in terms of prices. Both have nice ambience, although i do have to give chosun an edge on this aspect due to their outdoor seating area. but still, the food alone will make park's worth it.
If they're Korean, I'd say Park's. The meat is better but the atmosphere is not as upscale. Chosun Galbee is where you take white people you're introducing to Korean food -- not because it's inauthentic but because it's nice and decorated and the staff's English is better.