Not familiar with the Moody, but very familiar with the Pearson 365. My best friend bought a 365 at the 1979 Houston In the Water Boat Show and sailed it until he bought a farm and retired in 2005 - he sold it to help with the purchase of the farm. Between my Bristol and his Pearson we have sailed across the Gulf in every direction and endure some very bad weather in the process. Good solid boat, best layout for a chart table I've ever seen (you can sit at the chart table and talk to the helmsman), good galley for cooking at sea, strong underbody (cutaway forefoot keel and skeg hung rudder) easy engine access. If you end up with the Pearson, you won't be disappointed.
The original post was looking at a MORGAN 382 or a P 365, not a moody. I took a look at both of those boats in a search for my boat. I was looking for a boat that would take my girlfriend and I to the Caribbean for a year. Both boats fit our budget and size requirements.
I ended up with a 1976 P 365
Both boats have a lot in common they displace around 18000 pounds, have a similar waterline length, similar lines, high bulwarks, similar interior volume and similar keel design.
Here is my view of the pros and cons of each
Morgan 382 Pros
Has a quarter berth with a foward facing nav station (nice for guests)
Sloop rigged for easier short handed sailing and better pointing
Morgan 382 cons
Traveler mounted in the middle of the cockpit
Not as much head room (I am 6'4")
I think both of these boats are very similar and probably both great for what you want to do. In this economy I wouldn't spend a dime over 30k for a nicely equipped one of either in great condition. If it needs work you should be able to get it for substantially less.
Oh a Morgan! His original post stated Moody 383. The Morgan 382 is an excellent cruising boat. My buddy who we sailed with for seven years had a 384 (I think) always get the last number wrong but it's the same boat. I'd take that over the Pearson. Here's the Morgan. Took the pic as I was passing him. He just sold it last summer.