We've had our Leesa mattress for just under a week (ordered on Saturday delivered on Thursday). Leesa make them to order rather than do a next day so only say a 4-5 day delivery. The mattress arrived vacuum packed in the usual tall box, was lugged upstairs and unwrapped and allowed to decompress. The amount of plastic wrap these companies use is mad. Straight away I noticed that the outgassing that all these foam mattresses have was much less than the Casper. There was only a slight chemical whiff on the Leesa that faded quickly and was gone after about three days. The Casper was much smellier for longer.
The mattress itself is a pleasant light grey/oatmeal with some white stripes across the bottom. I believe the first versions of the Leesa had a one piece cover that couldn't be removed, the current design has an unzippable cover. Where on the Tempur and Casper you can unzip around the bottom and throw the top part into the wash, leaving the bottom half under the mattress, the Leesa zip only goes around the sides and top. This means that you unzip around three sides, then pull the top and bottom off together. I imagine that this is going to be a real PITA when removing or refitting the cover, and means some washing machines may not be able to take the top and bottom cover all together. I think there will be much pulling and tipping of the mattress on the odd occasions you need to clean the cover. It's a shame the Leesa doesn't have an extra 1.5 metres of zip to make it easier to wash.
The mattress itself is really nice. The top layer is two inches of Avena foam, which is a synthetic latex. Latex is supposed to have a nicer, cooler feel than foam, but is less durable, and Avena tries to duplicate that with better durability and vents to help heat dissipation and air flow. I found it gave nice spring, but allowed you to sink somewhat into the memory foam layer underneath, even though it feels fairly firm and supportive. The dipping of the top layer was much more localised than the Casper, so I still felt I was more into the mattress, rather than rattling around the bottom of a dish with no support as with the Casper. I also found it pretty cool, in that it warms rather than gets hot. The only time I felt too hot was first thing in the morning as I am waking up and my body temperature rises. This is pretty good given we've got a mattress protector, a winter quilt, and the central heating coming on at the same time. It's much cooler than our old Tempur. The Leesa also seems more comfortable and supportive when sleeping on my side or stomach than the Casper, but not as enveloping as the Tempur.
The layer underneath is two inches of memory foam that give the support and shaping deep down into the bed. You can feel that this part of the mattress responds more slowly and shapes to your body. Underneath that is the six inches of support foam for the structure of the mattress. The Casper has more support foam, and less of the comfort and memory foam. The movement isolation is also a bit better on the Leesa, and a person moving around on one side can hardly be detected by the other person. The Tempur has slightly better isolation again.
The Leesa is a bit more firm and has much more spring than the Tempur, though I'm sure one of the newer non-tempurpedic Tempurs will feel similar. The Leesa is a half-way house that tries to compromise between the spring and coolness of a spring mattress, and the squishiness and "sinking deep" of a traditional Tempur. You don't feel that you have to climb out of a hole when moving on the Leesa. The edge support is much better than the Casper, and at least as good as the Tempur, but the tempur has a sort of increasing density when you put your weight on it, where the Leesa has a kind of more solid spring. The whole thing feels like it has memory foam in it, where many other foam mattresses just feel like foam or try to duplicate a spring mattress.
The Leesa softens up as it breaks in, and I can see it's becoming more pliable on my wife's side, and now on mine, which I quite like as I'm hoping the Avena layer becomes more flexible and bends a bit more into the memory layer when you put pressure on it. If the Leesa gets a permanent one inch dip, it become eligible for warranty replacement.
TL;DR
So in summary, I like the Leesa vastly more than the Casper, apart from the expected infrequent annoyance when I have to remove the cover. The Leesa has thicker comfort/memory foam layers, a nicer, more localised spring than the Casper. It's more comfortable, cool and supporting, and does a good job of compromising between a spring and memory foam mattress. It's a little more expensive (about £40 than the Casper) but hugely cheaper than a Tempur. All the companies have a 100 night trial (if you buy direct) and they always seem to have discount vouchers on their websites to bring the price down a bit.
However they said they will honour their warranty and send me a new Herdysleep mattress as a replacement. 
