No, there will not have any speed difference, but you have unnecessary weardown, and an unnecessary chance of failure.
Traditional harddisks encode data with a simple pseudorandom generator, more modern ones and (virtually) all SSDs encode data with AES, always. The reason for that is that storing random data (or random-looking data) is much more favorable towards wear-levelling, both on magnetic and solid state drives, but in particular in the case of the latter (thus AES is first and foremost used to scramble bits, but as a free bonus, you can have security at no extra cost).
Thus, writing out a lot of zeroes effectively writes out a lot of "kinda random bits".
That's that, and it isn't in any way faster to read (or overwrite) one or the other either.
On the other hand, overwriting the complete drive means writing some billion sectors. While harddrives have (purely fictional) failure rates that are so low that they seem like "never happens", given the huge sizes of modern disks "never happens" is much more like "is kinda likely to happen". It is for that reason that for example RAID-5 is no longer recommended because the likelihood for encountering an unrecoverable failure while trying to re-sync after a failed disk is so high that it might become a practical concern.
What does that mean? Well, it means nothing in general, but overwriting the complete disk without need is probably not a good idea. Even for a secure erase, if that's intended, there exist nowadays much better (faster and more reliable) methods.