British · Patron XO Cafe
Patron XO Cafe is tequila and coffee rather than rum and coffee, and it is noticeably drier than Kahlua. It was built to be a dessert liqueur that does not taste like syrup, and that dryness is exactly what an espresso martini wants.

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The one thing that matters
Because it is less sweet, you may want a quarter ounce of simple syrup to get the foam right. Sugar helps the shake hold air, which is where the crema on top comes from.
Yes, and it makes a drier one than Kahlua. It is tequila-based rather than rum-based, so there is less sugar and a slight agave edge. Add a small amount of simple syrup if you want a thicker foam.
Kahlua is rum-based, sweeter and rounder. Patron XO Cafe is tequila-based, drier and more bitter. For a sweet espresso martini use Kahlua; for a sharper, more coffee-forward one use Patron.