I've never had broccolini.
I cook broccoli rabe (I like Andy Boy brand). Not sure if they are the same by you, but here they are two different types.
Andy Boy brand is nice and clean, so all I have to do is chop off the bottom inch or so of though stems and wash once or twice. I sauté fresh garlic slices in olive oil. Then throw in the washed broccoli rabe and a bit of water. Salt, ground peppercorns, and ground red pepper flakes to taste. Lower heat, cover pot. Let it stem a bit till it wilts and is just tender. Take cover off and toss a bit. Don't overcook.
From Google:
Broccolini is a sweet, mild hybrid of broccoli and Chinese broccoli with long stems and small florets, while
broccoli rabe (rapini) is a more bitter, pungent, leafy green related to turnips and kale, with small buds and leaves; think broccolini as a tender, sweet side dish and broccoli rabe as a robust green for Italian dishes, both delicious but distinct in flavor and origin.
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I like to serve/pair the bitter broccoli rabe with mild boiled and buttered potatoes or mashed potatoes. And a meat.
Sometimes I will cook potato cubes in the l/o rabe juice and add rabe at end barely warming it. Or I will just eat l/o rabe cold. I hate it overcooked and mushy.