Is there any downside snapping a picture (or scanning a copy) of every check when writing vs. using a duplicate check? Or is the picture/scan as valid as a duplicate if used later on as some evidence?
For me, the main benefit of using duplicate checks is that the copy is created automatically. If I had to take an extra step, whether taking a photo or writing on a stub, I would probably not always remember to do it. There is also the issue that you might need to write a check when you don't have your smartphone with you, or it is broken or has a dead battery, etc.
There are various pros and cons of having an electronic record versus a paper record. A paper copy of a check is more vulnerable to physical loss or intrusion, but an electronic record is more vulnerable to hacking. You also have to keep the images organized somehow, and take care of data security and backups for the images. You'll have to evaluate which is the greater concern for you.
A minor side point is that check duplicates often omit the account number and obscure your signature. A photo of the original check would include both of these.
As far as "evidence", it seems to me they're both equally good evidence that you wrote the check - but that's not really that useful. In most sorts of disputes, what you would need to prove is that you actually delivered the check to the intended recipient, and neither the photo nor the paper copy is evidence of that. You could have written the check, taken your photo / copy, and then torn it up.
No, there is no downside.
I personally don't use duplicate checks. I simply make a record of the checks I write in the check register. A copy of the check, whether a duplicate or a photo, isn't really proof of payment for anyone but yourself, as it is very easy to write a check after the fact and put a different date on it.
When banks would return the actual physical cheque, at least you had some printing / writing from the other bank on it, as some type of not-easily-Photoshopped proof.
Now many (most?) banks don't return the actual cheques anyway, just an image of it - sometimes a low quality shrunken B&W photocopy-like image too.
You'd have to check with a lawyer or court in your area, but I suspect any photocopy or image, as well as a written or carbon-copy duplicate, would not be good enough proof for a law court, since they could all be easily re-written or Photoshopped. So I don't think there's a real upside anyway.
Only an official bank statement saying that the name/people written actually cashed the cheque might be "good evidence" (I'm having doubts that the bank's own low quality "image" would even qualify, unless it's verified as coming directly from the bank somehow).
I'd agree with Nate (+1) that a big downside could be identity theft, either online or alongside phone loss/theft.