I have an older Peterson mill that I use mostly for my own woodworking.
It works great.
Advantages are -
Being able to handle big logs. When a bandsaw gets logs up over 30" it becomes a problem. 30"+ swingblade sawyers start smiling. No problem cutting smaller logs, but you wont get the production that you will from BIG logs.
Easy log handling . Big logs can be cut where they lay, no need to quarter them first or turn them on the mill as you saw. Just slice out your boards (flat or qsawn) from the log in layers.
Portability. The whole mill packs into a small tralier or the back of a pickup. You can set it up any place you can get to with a 4wd, quadbike+trailer etc or wheel it into a back yard by hand. Lets you cut those big logs that no one else can.
Low maintainence. Sharpening is quick and easy (5mins with the blade left on the mill). OK dirty logs will mean more frequent sharpening, and hitting metal can be anything between not noticing, having to sharpen.. or having to get the blade retipped.
It's a dimension mill, all the boards come off already edged. No need to edge boards later.
Down sides.. You cant cut REALLY wide boards. Double cutting will give you some 16" wide boards (on an 8" mill) but generally you are limited to 8x8
Smaller logs you need to set up some sort of log bunk and dogs to hold them in place. These aren't standard with the mills.You can cut smaller (12" ) logs fine, but you wont get the production that you would from 3-4' logs.
Thicker kerf means more sawdust. The bandmill may be able to recover slightly more wood from each log. This is partially offset by the swingmill accuracy, less miscuts from dull blades wandering around knots etc
As for the Lucas / Peterson thing, I prefer the Peterson, but then I'm biased. The Peterson is easier to doublecut with and I think the construction and materials are better. They also produce higher end swingblades with more automation (and more $$ of course). But I'm not running the Lucas mills down, they work great and are well supported in the US by Baileys.
Cheers
Ian