For longevity, I would recommend embroidering directly on the jacket. It will easily last as long as the jacket when embroidered directly.
For comfort, I would make a patch and sew on the patch. When you embroider directly though a jacket, the back side is rougher than the original denim, and it can be uncomfortable. A patch can also usually be made bigger than it would be possible to embroider directly.
There is usually a cost difference too, because you have to ship around the jacket, and if the embroidery ‘goes bad’ such as splitting a needle or tearing the fabric, you will wreck the jacket and not just the patch.
Lots of tradeoffs, I have done both and it depends on lots of factors. Large patches are definitely more popular than direct embroidery on jackets. It’s a different story for other clothing (hats, sweaters, pants ets) and smaller areas such as a pocket on a hoodie or on the hood itself.