I think there has been some cross-purpose talk on this thread of which I am also guilty. The following excerpt from the Avsim review sums up the difference between ASE and REX well:
Because of all that, there are a number of different ways to go about enhancing the way FS deals with weather depiction. You could add a custom cloud set to it, which will not affect how FS interprets weather data, but will improve how the weather data it does interpret will actually end up looking in the sim. Alternatively, you could add a utility which has a more sophisticated weather engine, which would improve the way FS interprets the weather data it has to convert into a simulation of what you see in the sky and experience in the wind and turbulence.
For these different aspects of FS weather generation and depiction, there are some utilities out there which do everything, one such being REX (Real Environment Extreme), which adds custom high resolution cloud sets as well as its own weather engine, so it is a one stop shop for enhancing the weather. But Active Sky Evolution is more focused in what it does than REX, concentrating on purely on how the weather is interpreted. Thus there are no graphical cloud set enhancements with ASE (it will use whichever ones you have installed), as it simply concentrates on reading and depicting weather data better than anything else out there, and it has to be said that it is massively capable in that regard.
Thus the typical ASE user is likely to use it in combination with an enhanced cloud set, although they could just as easily use it with the default FS clouds if they wanted to. Many choose to use the enhanced clouds sets which come with REX, but forgo its weather engine and instead use the superior weather interpretation capabilities of the ASE weather engine.If you are after pretty graphics with a weather engine that is better than default, then REX is the one.
ASE is purely a complex weather engine, without graphical enhancement (although default clouds look better anyway, bit like the Orbx weather themes!), but will operate with addons such as REX.
As a 99% VFR sim pilot, (and a real life paraglider/paramotor pilot), accurate down in the weeds weather is more important than good looks to me personally, hence why I went with ASE (I had already heard the negative stuff about ASX, and although it was on special, figured that ASE would be the right choice for me). As with anything, check out the pros and cons thoroughly on as many forums as you can find before comitting hard earned cash to it.
