I have No experience of the Leigh jig, but have had a wood rat for >20 years. I bought it with dovetails in mind, and it does work well for that purpose. I suspect that if you just want a device to give you perfect fitting dovetail joints every time, then the Leigh jig may be easier and more foolproof, but I wouldn’t trade my rat for one. I haven’t had to junk any piece of work I have done on the rat, but because you make pencil marks on the face of the machine and align things to that it requires the same good eye and marking as most other woodwork you do. It’s kinda up to you to do something tight fitting or a little looser. The single thing I have used it for most is for making shelves with the shelves fitted by way of a long sliding dovetails. i have done hundreds of them. They are easy to do, and the result is superb. The photo shows a pair of fully laden bookshelves made with cheap pine. none of my shelves ever sag using this method, as any one wanting sag would mathematically require all other shelves to do similar. Using just two long shelves for a shoe rack, one can sit on the upper shelf in the middle, and there is no give. I doubt any other construction method would hold together. They have other uses too but that is my favourite.
Stuart