Security wise, it's the same, assuming you do not disable verification on the conversion process (which speeds up a lot, but then if there are problems, they won't be detected).
Speedwise, it varies. Typically, syncing is faster, as this can do some things in parallel. However, if your internet download speed is pretty slow, or if you can't download much (e.g., you have a data use limit on your internet connection), converting might actually be faster or favorable.
Syncing also has the benefit of having known block hashes for the first million blocks or so, and avoids some checking if hashes match the expected hashes. This is safe, due to hash function properties, and also a fair bit faster. You'll also have to sync about 8 months of blocks afterwards anyway if you choose to convert.
So, in a nutshell, I think your're best off syncing from scratch.