My two cents:
(bear in mind I’m not a aleph nor a audio dev and have spend little time with it)
While they share some similarities (user programmable dedicated audio machine, separate control and audio backend components. nice screen and beautiful objects altogether. best friends of grid and arc), the experience is quite different.
With bees, alephs control editor, you can make apps by stacking and connecting operators, on the device itself. No code writing needed. Though the result is a list that is hard to read next time you want to modify something. Since it’s open source, nothing stopping you from replacing bees with something different altogether, which gets more involved, think monome eurorack module alternative firmware. The audio dsp component, running on a blackfin micro processor, is said to be cumbersome to program (no floating point processing unit).
Compare that to a relatively simple syntax and framework with lua and supercollider as audio backend, a widely spread audio dsp language. On aleph you have to swap sd cards, vs. matron running in a web browser, wifi+ssh.
It can be easily seen that monome took the vision and experience from making the aleph and improved a lot of the aspects and made a way more approachable and accessible device with norns. It produced quite a few programmers this past few years 
That said, aleph is bare metal (dedicated micro processors instead of full blown linux machine), which means ultra minimal latency. It has CV and more audio io.
Also Aleph is an even more impressive device to touch imo and is built like a tank, that of course also means heavier and more expensive.
Norns has battery.