I have a Lucas Mill, which I may possibly be selling soon. I also run a bandsaw mill which I am not selling.
As for which you should get that depends on firstly the logs you have and secondly the timber you want.
If you get large logs you will be struggling with a bandmill. Even one like mine with a 28" cut will only comfortable handle logs up to about 2 feet diameter, or if bendy then even less. Yes I know the advertising states that a 28" cut bandsaw will handle logs up to 36 inches but this assumes they are perfectly round and perfectly straight. Also they are just too big and heavy too turn, so it is just easier to get them under a swing mill (Lucas[Peterson) or if they are monsters even assemble the mill around them. I have milled logs up to about 8 tons in weight with my Lucas - you cannot do this on a bandmill, unless you get a massive industrial one. On the other hand, loading lots of small logs onto a Lucas mill is very inefficient.
So in summary, large logs you want Lucas Mill or Peterson, and small logs you want bandmill.
And the other factor is the stock you want. A bandmill can produce wide boards - well about 18" to 24" so pretty wide. This is great if this is what you need. A Lucas Mill will produce boards up to 9 inches or so (varies a little with the model) but they are square edged. In theory this is possible with a bandmill but in reality they will be far less accurate and less square and it is a lot of extra handling.
If you want square edge timber go Lucas/Peterson. If you want wide boards go Bandmill.
I forgot to say the Lucas mill can have the chainsaw slabbing attachment fitted (and I do have this) but it is really only for occasional use. It will indeed produce really wide boards but it requires a lot of effort compared with a bandmill and lots of tooth sharpening. So a good extra but not something you would use daily.