Exactly, if someone with >50% power can essentially double spend it makes the currency as a whole almost worthless. As a result it's very much in the creator's interest to either not have >50% or to come up with a distributed consensus algorithm where a majority party can't double spend (very hard).
That is the difference, but what is the value in that? You're making things much more complicated and for what - especially for an in-app currency.
It depends on the value of the backups I guess and the total cost involved. If you're looking at store of value there needs to be backups of backups. I see room for both depending on the needs of the business. It's just a trade off -- the blockchain is inherently more stable and secure than a server for certain purposes and server is far faster and cheaper depending on how you use it.
In a word -- decentralization -- is the key difference between a virtual currency described by some SQL tables and an API and one described by a blockchain.
A gov if it wants can take down a server if it is physically hosted in that country. A blockchain unless you've gargantuan CPU power is nigh on impossible to take down.