Both good choices, actually all three:
I have owned a 1979 37C and presently I own a 1988 36 Sedan.
Others on the forum can talk about the 36 series 1 which seems to be the most popular of the three models in question.
The 37 is the heaviest of the three by far, has the widest beam and the biggest cockpit. It's wet, noisy, very solid, easy to maneuver, and fun to own. There is some teak to maintain but for the most part it's an easy keeper. It requires a great deal of power and in the 671 N configuration it's just plain slow, but you can go when others can't. The interior is nicely laid out, all are galley up, but the main salon is tight. On the other hand the two state rooms are spacious as is the head. Engine room access is poor for a normal sized human, it's really tight. I had the worst time trying to get to the outside of the engines, battery and A/C service is a real issue. As mentioned the bridge is quite spacious, has a bench in front of the helm and one to the starboard side. I really liked mine had it for 5 years and everywhere you went people thought it was at least a 42. I wouldn't hesitate to own one again. It would be nice to find a 1981 with the queen berth in the master, but they are rare.
The 36 is quite a bit different. It's much quieter, both the engines and the hull. The 36 has cored hull sides where the 37 is solid glass, they sound and feel different. The 36 is a true deep V where the 37 isn't. You can't get the 36 to pound no matter what, it always lands softly, and it's much dryer than the 37. The engine room is easier to access and there are three really big hatches that allow you to gain access easily, although the battery outboard of the starboard engine is hard to get to but not as hard as the 37. My 36 is noticeably faster than my 37 although I have modern diesels with 40 more hp each. The old onan in the 37 will wake the dead and there is no room for a sound shield. My 36 is the model with a very small cockpit, I'm up north and it works great for my application. The series II has three available layouts, you can check them out in the brochure archives, I have the biggest interior and it's actually somewhat bigger than the 37. But in all fairness to the 37 mine is a single state room, galley down, dinette model, it's very open, and because Hatteras moved the cabin house back on this model it really stretched the main salon. The actual dimensions are 36 7' with a 13' 7" beam, I think the 37 was just that 37' with a 14' beam. If you want to fish or do a lot of entertaining in the cockpit my boat is the wrong one. If you cruise, and there are just two of you it's ideal. The 36 has more angular lines, a few differences but unmistakably a Hatteras. With a good set of diesels both the 37 and 36 are worth similar dollars. In my opinion for a very fair price you get a super boat that will never let you down. Mine is fresh water too, stored indoors in the winter and out in the summer for 4 months, I wish I lived in FL, just not in the cards yet?
Tony D