Welcome to the Backwoods forums and I hope we can provide the answers you are looking for as there is a great bunch of people on this forum. I also like the cookers you own and do have all of them in my stable.
The Backwoods line of cookers are somewhat like your Egg cookers and do have multiple ways of cooking, smoking, grilling, and baking and are fairly close to being air tight which gives you many options on how you can use them. In other words, anything you can do on an Egg, I think you will find that you can do the same on a Backwoods. From smoking cheese at 80 degrees, to smoking sausage or fish at 115-140 degrees, and then your normal low and slow type of cooking at 225 275 degrees, to medium heat range of 275-350 for poultry, casseroles, and others, to high temp baking at 375-425 for breads, pizza, and again poultry, to probably over 1000 degrees with the removeable water pan and grilling at the tip of a lump charcoal flame, these cookers can flat do it all. Check my webpage for details.
Now, I need to correct my friend Ricks post as I think he probably misfigured the cooking area of the cookers.
The Backwoods Party has more cooking space than the Fatboy by 13-1/2 sq ins. 6 Racks @ 15-1/2X16-1/2 VS the Fatboy with 4 racks @ 19-1/2X19-1/2.
The Party gives you more options for cooking with the much taller cooking space and the extra 2 grids.
Ok, lets look at what you want in that new cooker.
"I will be using it in the backyard for the most part and will cook for anywhere from 5 to 10 people most of the time."
Any of the cookers will work well for this and of course, the smaller cooker would be more efficient and easier to handle.
"But also I do some big cooks a few times a year anywhere between 80 to 125 people."
The Party, Fatboy, and the Competitor will cook for 125 people very easily if you control the menu. Heck no, you can't cook a half slab of ribs each for 125 people but again, you could do a nice cook with other meats. A fellow can also do some cooking in advance for the larger cooks. (Just like you probably do on your Eggs now!)
All three cookers are good for competition cooking. I have cooked competition with all three of the cookers and I like the Party the best for KCBS cooking. It is just so much easier to handle for this old feller.
This info should get you started and please ask more questions and we will try to get you answers.