Nika, The Cake Bible states that the mousseline holds up better than any other. The Silk Meringue holds up well (better than the classic), but not as well as the mousseline.
What flavor are you using? I prefer the silk meringue for the caramel variations (caramel, praline, coffee-caramel and burnt orange) and for the apricot. I prefer the mousseline for fruit curd flavors, liqueur-based flavors, or for when I want to be able to add in a lot of fruit puree (like Hector’s strawberry version, or raspberry).
In addition to flavor and temperature resistance, there’s also the color- mousseline is paler/more white, while the yolks in the silk meringue give it a more yellow color.
You said, “creme anglaise seemed to be greasy and the milk solids seem to separate,” which makes me wonder if maybe the custard was heated too high? It needs to be higher than 160F but not over 180F or the eggs will curdle. Also, it needs to be cooled to room temp before adding to the butter. You didn’t deviate from the recipe and add butter or oil to the custard, right?
Is it possible that you are making one of the caramel flavors and adding the milk to the caramelized sugar? If so, anything that makes the milk-sugar mixture too acidic can cause the milk to curdle- this includes having the caramel too dark (it gets more acidic as it darkens), using brown sugar, or using a milk product other than regular, ultra-pasteurized whole milk.
We’d love to see some pics of the final product!