Okay, so I did a passably careful experiment.
Front row, left to right: emulsified snail butter sauce in which snails braised 3 hours; emulsified snail butter sauce braised without snails 3 hours; fresh normal snail butter
Back row, left to right: snails braised in snail butter 3 hours, snails braised in water, white wine, and a dash of Pernod
These were then turned into 6 kinds of stuffed-shell snails:
1. Butter-braised snail, snail-braised butter
2. Butter-braised snail, plain braised butter
3. Butter-braised snail, traditional butter
4. Traditional braised snail, snail-braised butter
5. Traditional braised snail, plain braised butter
6. Traditional braised snail, traditional butter (classic escargots a la bourguignonne)
This is in order of preference. My family did not like traditional wine-Pernod-braised snails. They did not like the way traditional snail butter breaks. They liked the weird, woodsy flavor of snail butter in which snails had been braised. I liked them all, but I did think that the hint of anise clashed with the plain braised butter. Otherwise, I'm easy.
Note that the "emulsified snail butter" is not simply butter. To make it, I worked backwards, but it shouldn't make much difference which order you go.
Braising: put butter, parsley, garlic, salt, and pepper in a heavy-duty zip-type bag. Seal tightly using the water-displacement technique (lower the bag slowly into water, letting the water pressure drive out the air, then seal). Cook sous vide at 140F for 2-3 hours. Snails may be placed in this from the start to make the snail-braised butter.
Emulsification: for every 100g butter, put 50g cold water, 1.75g agar, and 2.5g xanthan gum in a saucepan. Heat while whisking constantly, until it all dissolves completely. Cool to room temperature. Warm the butter so it is liquid. While blending the water solution with an immersion blender constantly, slowly pour in the warm butter. It will emulsify to a light hollandaise consistency.
I did emulsification first, then braising, but that was because I was doing other experiments; it should be a good deal easier to go the other way.
NOTE: Be very attentive to salt. I found that my emulsified butters weren't quite salty enough.