No. The version doesn't affect the speed of download. Your internet connection and your peer's internet connection does. The synchronization time is also dependent on your hardware speed.
If you are running Bitcoin Core below 0.10.0, you won't download as fast as the clients above that. Bitcoin Core above 0.10.0 uses headers-first synchronization which is significantly faster.
I'm used to run full nodes but I never experienced such slowness while downloading the blockchain, my hardware is definitely not that good but that doesn't explain why It used to download just fine before and I'm using 0.13.1 by the way.
Almost all of the time, the bottleneck is with the verification process as opposed to the download process.
IIRC, Bitcoin Core 0.14.0 does have significant improvement over the previous version in terms of the verification. Consider upgrading.
Anyways, you can always increase the dbcache to get the synchronization to speed up.
