Interesting.  Here's my version of the scenario.  
A couple of weeks ago I bought the Samsung Galaxy Note Edge on Verizon as an upgrade.  It totaled just about $500 with the upgrade fee ($30) and taxes.  The phone was defective, and ultimately it was returned.  There's quite a story with that, involving several stores and speaking with the Executive Office, but that's not the point of this post so let's just say I returned the defective device and was returned to my pre-upgrade status of being eligible for an upgrade.
I went into a Verizon Wireless store two days ago, ready to purchase the Note Edge again as an upgrade.  That would come to $500.  My current service plan is about $100/mo for 4GB/mo of data.  Over the course of two years, this would total $2900 (500 + 2400).
The sales rep then tried to sell me on the Edge plan.  He was successful so far, as it was literally past closing time so I didn't have a lot of time to research this, but I did get the manager's assurance that if I rather go the upgrade route, I can do so without any fees within 14 days.  The Edge plan... 
1) It would increase my monthly fee by about $10 while increasing my data allowance to 10GB.
a) My new monthly fee would be $110.xx
b) My monthly data would increase to 10GB/mo
c) I would be charged $33.33/mo for the phone ($800 after 24 payments).  I don't know where the TAX on this comes in, or if it's already built in to the 33.33/mo (ie, if the $800 retail price was including tax).
d) I would get $25/mo credit (which he says continues after the 24 months if I stay with this phone).
2) The net cost for the phone would be $33.33 minus $25 credit per month = $8.33/mo ($199.92 over 24 months).  
a) That's much less than the $500 it cost me to buy it as an upgrade a couple of weeks ago.
3) Over the course of two years, the total would be $2640 (800 for the phone + 2640 for service)
a) That's much less than going the upgrade route, which came to 2900 (see above).
Assuming I keep this phone for 24 months or more, the phone would be mine and I would not have to trade it in to do another upgrade.  If I wanted to upgrade then, I would start right over with the unsubsidized price of the new phone split into 24 monthly payments, and this current phone I just bought remains mine.
I kept wondering what the catch was, believing that no merchant or corporation would offer something for nothing.  But in my scenario, I can't find a catch.  It seems to be a better deal to go with the Edge plan, IF I keep this device for two years.  
Where there might be a disadvantage is if I upgraded early.  If I trade in the current phone after 18 months (after 75% of the retail price is paid off), I would lose the equity built in the phone, as I would have to trade in the phone and wouldn't be able to sell it on my own.
a) This reminds me of rental cars' pre-purchased gas option.  If you pre-pay for a full tank of gas, you can bring the car back at any gas level.  If you bring the car back nearly completely empty, you may come out ahead if the pre-pay cost for the gas was lower than what you could get on your own.  In this case, you win.  If you bring the car back relatively full, you do NOT get a prorated refund from the cost you pre-paid.  In this case, you lose if the pre-paid total cost was more than it would have cost for you to top off the tank.
I signed up for the Edge plan, then went home and began pouring over the web to find articles or posts to help me figure out which move was correct...to just upgrade, or to join the Edge plan.  
A lot of articles that talked about it being a WORSE deal for customers mentioned that the normal monthly service fee already has a phone subsidy fee built in.  In other words, if the monthly service charge were $60, maybe up to $20 of that was charged to pay back the subsidy that may have been provided to the customer when the phone was purchased, while the remaining $40 is the true cost of the service.  These articles argued that your monthly service charge already INCLUDES a charge for the phone (ie, the recoup for the subsidy on the phone purchase), and then the Edge plan charges you an ADDITIONAL cost of the phone split into 24 months, so you are paying for the phone TWICE.  But the flaw in that argument is that whether you upgrade, or do the Edge plan, your monthly service charges are THE SAME anyway (which is actually LESS with the Edge plan if you factor in the monthly credit of $25, as it is in my case).  
When you go the upgrade route, you pay the subsidized price (instead of retail price) of the phone, plus an upgrade fee.  In my scenario above, going the upgrade route cost more after 24 months than the Edge plan route.
If there is something I'm missing that makes my assessment invalid or in error, please let me know.  I can still switch back to the upgrade route within 14 days.  I purchased this device on Fri; it's now Sun.