I have both the "Nextel" Sprint, and the verizon PTT. The Nextel is a work phone, and my Verizon is personal (family & friends). Both have good features, however the Verizon use area is much larger than the Nextel is. Most of the posts are right, ie, you have to have the persons phone # on Verizon, and you have to have the DC # for Nextel. They are not compatable with each other.
Nextel has a "copyrighted" chirp, but Verizon does have one of it's own. It has an "alert" function just like the Nextel. Both are basically the same, but different in some ways.
I believe that this is just the beginning of the PTT market. Soon other companies will have their own, and will probably not be compatable. Seems silly though. If all the other companies want a share of the PTT, and compete with Nextel, they should consider compatability.
Now back to the the question. Which works best? Well, If you have "Sprint", the cell call quality is poor! The phones are more expensive, although they have, at this time a larger selection. Verizon at this point and time has the Casio G3 Boulder, and the Motorola 750 Adventurer. I have the Motorola, and my boys have the Casio. Both are good phones for PTT and Cell phone calls. The Casio is great, it is waterproof, and almost indestructable. The Motorola is shock proof, but is not completely waterproof. The ratings have been so so for both phones, but I am testifying to you now, that both phones are good to excellent in my use.
The Casio's battery life is not as good as the Motorola. Consider getting the extended battery.
I think you will see that Nextel has their work "cut out" for them to compete in the next years. Although Verizon does charge you $5 per month, per phone for PTT, the quality of the calls is worth the price.
My vote for now, is for you to go with Verizon. You have a 30 day time trail, and if you're not happy, you can return it without charge. Test it for yourself, and good luck. Hope I helped shape your decision on which to try!