Alan, I could write for a long time (edited to add: it looks like I did.
) regarding the benefits of the Rat for dovetails over the Leigh jigs. I'll try to keep it short.
First, consider why you want dovetails. Is it because of their appearance or for joint strength. If the latter, I urge you to consider other methods of joinery. With today's adhesives, I think you can come up with less fiddly and quicker ways to join two pieces of wood at the corners that will be just as strong once glued up.
If you are making dovetails for their appearance then consider the difference between carbide and HSS cutters. Personally I think carbide cutters make fat, ugly dovetails. That's my opinion of course but compare them to ones made with the WoodRat cutters and I think you'll see the ones made with the HSS cutters look much more pleasing.
BTW, you can certainly use carbide cutters with a WoodRat. You are much more limited in cutter choices with the Leigh or other dovetail jigs.
Also consider the width of stock each can take for dovetailing. Maybe dovetailing wide stuff won't be an issue but if you want to do a blanket chest or other wide case sort of thing, you might find you have to do some fancy footwork to make dovetails with a Leigh jig. The D4 is limited to 24" and the 1600 is limited to 16". the WoodRat can handle about 32 or so out of the box and could easily be set up to handle wider stock if you really wanted to.
Batch cutting is easy with the WoodRat. The tail boards can be stacked and the cuts made quickly.
The Leigh jig will consume bench space when you are using it and needs a home for storage when you aren't. The Rat hanging on the wall is always put away and it is always ready for use.
This next part of the argument doesn't always work for people because they may already have covered these operations with other equipment. But, the WoodRat can do almost any operation you'd do on a router table. You can do mortises and tenons (safely climb cutting for a cleaner shoulder, too.) You can make dowels, too.
Both will do sliding dovetails but can the Leigh jig cut sliding dovetail sockets in the sides of a pedestal for a table?
I guess it depends on what you want out of the dovetailer. When I was deciding between Leigh and Rat, I got all the way to entering my credit card number on the Lee Valley site for the Leigh D4. I decided I should take one more look at the Rat and went that way. I'm happy I did.
This was posted before but here is a recent example of dovetails I cut with my Rat and a HSS cutter. Soory about the size.
Also edited to add: The stock in the this photo is 3/4" thick. In carbide cutters, it looks like the skinniest one that would handle the thickness is 1/2" wide at the bottom. This one is only 3/8".