as an example on the cordless bit, the Dyson V11 has 25v battery at 3.6Ah capacity, so that is a maximum of 90Wh of useage.
If it the vac ran for only 10 minutes on a charge than thats a max of 540W but, Dyson quote 20 minutes so 270W of suction (and all motors are in the 90% efficeincy range so no gains of note here). Compare that to say corded which typically has the EU max of 1600W, and its easy to see why the cordless convenience cannot match the corded power
I fail to understand the fascination with cordless stuff. It will always be limited by the laws of physics.
Same with lawn mowers. Work out how much energy a decent lawn mower needs to cut a lawn and then tell me they can fit that in the battery!
Battery tech works very well in devices where other energy sources are awkward and where intermittent power is needed, even at quite high power levels, but no good when you need continuous high power. My Dad recently bought a Stihl battery chainsaw, and it's a great bit of kit. The 2 stroke probably trumps it for power on a really thick trunk but I know what I prefer climbing a tree with!
Vacuum cleaners, though? Nope. I probably use it once or twice a fortnight (I'm not house proud!). I plug it in once to do the upstairs, and twice for the downstairs. Hardly enough inconvenience to warrant a crap battery model.