Oh! Itâ€™s likely a different form of possession or a matter of experience. He probably isnâ€™t just implanting his heart, but his entire heart and soul into the people he body-snatches in order to completely take over their bodies as his own. Itâ€™s clear heâ€™s done this for eons, so his technique is perfected as he moves on from body to body whereas Xehanort hadnâ€™t started his body-snatching thing until he was an old man.
I doubt that Luxu even takes the soul with him and instead uses the soul that already is present in the target body.
Because the soul is the very reason Luxu does all this in the first place.
In the KH universe the soul is a battery of lifeforce which maintains the body and allows the heart to control it and use it to interact with the physical world.
As time goes on and the body ages due to use by the heart, the soul slowly but surely spends the lifeforce it has and the possible ability to replenish/recharge it wanes the longer it is used, just like a real-life accumulator works.
Once the souls energy is fully spend, death occurs and the body is gone for good, only the immortal part (heart) remains as described in the KH 2 reports.
So Luxu taking the soul with him when hopping bodies would be counter productive as it would be a nearly spent one. He needs a "fresh" or still largely full soul to continue on in the physical world without interruption.
I do think however that the technique Luxu uses is different and probably on a higher level than Xehanort's by far as well. While he was not a chosen Foreteller he is one of the first six Keyblade Masters to exist so he most likely has access to and knowledge of ancient arcane abilities not even Xehanort was privy to.