Well, yes, John does have great delivery, what I'm trying to say is that Paul has a better voice. Not how he uses it, but he is more naturally talented. Delivery is important, but it's much more impressive if you have a good voice to begin with. I do agree with you that Paul sometimes sings too high, but he has more than just range. I feel he has a much warmer and richer tone to his voice than John. His early vocal performances are so effortless, whereas you can really hear John straining to perform. Of course John's style of delivery is much more suited to rock and roll, but rock and roll was never really about having a great voice.
Don't get me wrong! I love John's singing! It's perfect for the kind of songs he writes. But there is a difference between being a good singer and having a good voice. Freddie Mercury is pretty much the golden standard for this sort of thing. Not only did he have an incredible set of pipes, but he knew exactly how to use them. Paul and John could both learn a lot from him, methinks.