There is no guarantee that an owner will feel more bonded with a horse than the person who part leases it just because he owns it. It depends a lot on who spends the most time with the horse. But, I think there IS a difference. I have not been able to own, and have leased for many years. It' works for both me and the owners,and I am not really unhappy about it, but I would feel quite differently about the horses I ride, if they really were mine. There IS a difference when you KNOW it's yours, and when you know it's not.
I care about them and treat them lovingly, but it is not the same when I know that I will not be responsible for them until their dying day, and I cannot really say "MY" horse. And when the horse has some behavioral issue, I do not feel quite as driven to correct it as I would be if this were my horse. I tend to be more of "well, he's not mine, so it's not my right nor responsibility to change him." I am a bit lazier since I am just going to ride him, and put him back. I don't personally stand to gain from putting a LOT of training energy into him, since I may or may not be riding him 5 years from now. There's a sense of impermanence that makes me more accepting of flaws; kind of like the renter of a house might not be as enthused about remodeling it if it's serving his purposes well enough now.
And lastly, as a leasser, you really DO have to restrain yourself from falling in love with your horse. He isn't YOURS, so you cannot allow yourself that.
Still, I am really very fond of the horse I lease. I am THIS close, in my heart, him being "mine".