You do realize that the music often specifies bow direction? For short staccato phrases you often bow down on all notes.
Please do. And at full speed. And hit the strings hard. That's they key.
Here's why it sounds different; when you down stroke you are also pushing the string down towards the body. This is especially true when plucking hard. Up strokes tend to lift the string. You can't get that slamming tone up picking.
I know how to use a pick. I've been doing it for 42 years on both bass and guitar. I have no issues with my wrist. I'm also very good at cross picking. When I'm playing fast intricate parts I tend to start on an up stroke. Robert Fripp does as well.
But that's different from playing something like the Ramones where you really need to hit the strings hard to get the right tone.Or chugging along with a solid 1/8 note pedal. That sounds better with all down strokes. Or one finger.
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Another very simple but effective example of this is Adam Clayton's most memorable bassline, "With or Without You".