Here are some pics side by side so you can see the differences!
Minka on the left, Leslie on the right (black). I think they're both large, I know the Minka is for sure the Leslie I got second hand.
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Deets Pictures
Inside Main Compartment
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(Sorry she's full!!)
Handles
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(See below attached for Minka Handle pic as this one didn't load correctly for some reason)
Secondary Compartments
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Personally I like the Minka better than the Leslie by a smidge. This Leslie didn't come with the option of the long strap (I'm pretty sure the large one didn't), and I've never attached the long strap to my Minka because she sits well under my arm.
If I had to choose a style I would go Minka, I rarely reach for this Leslie unless it's raining, mostly because she came to me in worse shape than described by the ebay seller and so I don't worry about her as much when it comes to the elements. I find having to zip and unzip the Leslie constantly is annoying too and trying to dig around at the bottom can be time consuming, on the other hand the Minka slouches more than I like so she looks a little sloppy when she's sitting around!
I just realized my pics aren't completely helpful but I hope they are to a point! The above poster is right thought that the minka's main compartment is under the flap while with the Leslie you have to unzip the flap to get to the main compartment.