I am having trouble finding an answer. I'm not sure if butter cream or royal works better with stencils. Which one gives better detail? TIA

I'm no stencil expert, but I believe you can use either. Just be sure whichever icing it is is stiff enough that it won't "bleed" through the stencil.

I can't point you to an exact cake. But if you check the posted photos here of stenciled cakes, there are descriptions of how it is done. I do remember reading some of them and they stated which type of buttercream/fondant and if they used royal icing or buttercream to stencil over the cake.

HTH

I asked a similar question after I recieved some stencils for Christmas. I'd say the verdict was split - half use BC, half use royal. However, one person did mention that since royal dries hard it's easier to use if your stencil needs to go all the way around. You don't want the stencil to touch wet icing, so if it's dry you can make sure the pattern matches up without ruining it. I only stenciled once and used BC. It worked just fine. (no edges to match up)

You can use both. Just make sure your consistency is OK. Do a small test. You can have even use chocolate to stencil. Its all about consistency.

I think the use of buttercream vs RI with the stencil depends on how the cake is covered in it has a buttercream surface I would do Buttercream stencil if it is fondant then do RI stencil.

either one works great for me....

I have used both too, on top of buttercream I prefer to use buttercream.
Edna

I use buttercream on buttercream and royal over fondant. Both work well.

The cake will be frosted in butter cream. Would make sense about being easier to decorate if the royal icing is dry. I was wondering how they wrap the stencil around without messing up what you have already done. Do you find it makes a difference? I was planning on smoothing my cakes with a printed paper towel will the stencil still work?

Smooth the cake and let the frosting set up then wrap the stencil and use buttercream with the stencil. Not sure what you mean by letting the royal icing dry?