Well, that's not the path I chose. So I'm looking for what to do after the bitcoin sync finishes.
When the sync is done, shut down Bitcon-Qt.
Find the data directory for your operating system:
https://en.bitcoin.it/wiki/Data_directoryThis is where the current wallet.dat is located.
Remove the current wallet.dat from that data directory, and replace it with your backup of wallet.dat.
Start Bitcoin-Qt back up. It will scan through the blockchain that you've downloaded and search for any unspent outputs to addresses in the wallet.dat that you just installed. Depending on how fast your computer is, this can take anywhere from a few minutes to a few hours.
Bitcoin-Qt should then display your old bitcoin addresses in the "Receive" section and show the entire balance of bitcoins that you can access with that wallet.dat.
Or is the blockchain method a better one, aside from being faster?
I guess that depends on what you mean by "better". It is certainly faster and easier (seconds or minutes instead of hours or days) . It's possibly slightly less secure, but not enough less that I'd be worried about it.