I have never tried it, so it might be better, but I don't know. I am not going to find out, either, because I know that donating the primary and having the alternate hanging from a bungee cord around the neck is better than either of those.
When you have the alternate stowed in the traditional way, whether right or left, it hangs from some sort of system designed to release it easily when it is needed. That's the problem--it does release easily, even when you don't want it to. I can't estimate how many times while I was teaching that system that I had to pause and get a student to put the octopus back in place before we could do the exercise. I was already using the bungee system on my alternate for tech diving, but I had not made the switch on my recreational diving setup when I read about a horrific story of a woman who died diving near the Netherlands. She went out of air and went to her buddy for his alternate. Unfortunately, it had come loose and was caught behind him. As they struggled to find it, she inhaled water and drowned. That's when I went to the bungeed system for recreational diving, too.
In contrast, the alternate around the neck is designed to stay there, so it does not come loose. You donate the one in your mouth, which takes a fraction of the amount of time it takes to donate a separate alternate. Then you calmly slip the alternate on your neck up into your mouth--simple and foolproof.
When teaching the use of a separate alternate--whether right or left--you have the question of whether to teach students to reach for the alternate when they are out of air, or wait for the donor to give it to you after you signal. Some instructors teach one way, and some teach the other. In real life, the method used depends upon the OOA diver, who will either reach for the alternate or signal and wait. When I have done the OW checkout dives for students I did not teach in the pool and had buddy teams that were taught differently, each one usually did what they were taught. In most of those cases the OOA student reached for the alternate at the same time the intended donor reached for it, and in 100% of those cases, they knocked the regulator out of each other's hands and then essentially fought each other to get it back.