With Verizon there currently is not much of an advantage in month-to-month vs. contract, however there are some definite advantages in the contract.
The only advantage in a mont to month is that you can leave whenever you wish.
The "advantage" to the 1 or 2 year contract is that you get your phone at a subsidized price. The cost of a phone without contract is going to be approximately $200 to $350 more than with a contract. The reason is that the subsidized price is "made up" by about $15 to $20 of your monthly bill going to "pay back" Verzion for "loaning" you than $200-$350 to buy your phone. Even if you opt not to take "advantage" of this loan, your monthly bill will NOT decrease a single cent.
If you buy your phone at retail, and do not use the "subsidy" you are in effect "giving" Verizon an extra $15 to $20 a month.
If you have T-Mobile coverage in your area, and where you normally travel to (I do not, unfortunately) and you wish to not be tied to a contract, give them some serious consideration, because once you are out of contract (or buy a new phone at retail) they have "discounted" monthly plans that you can use that will save you $15 to $20 each month (and they are less expensive than VZ to start with, even with contract.)
I'm not knocking Verizon, I have them and am happy with them, however, with the exception of T-Mobile in the U.S. all cell companies play this "cheap phone subsidy" shell game. They absolutely LOVE it when a subscriber does not opt to get a new phone at a subsidized price when they are eligible for one, as it is just more profits for them.
In Europe, it's common practice to buy your phone from where ever you can get the best price on it, and then pick your carrier based on the best monthly price. Pretty much every carrier has split pricing for "subsidized" vs. "unsubsidized" phones.