When should I choose Daedalus over Butterfly (or vice versa) when playing as Sniper?

While the math provided by bunyaCloven is great, I think you should consider one more thing when choosing between Daedalus and Butterfly. In terms of personal damage, Daedalus is obviousy better, while Butterfly is more of a defensive item that still provides a great boost to damage output. However, Sniper can produce two illusions with Manta (which is mentioned in the question), which benefit much more from Butterfly compared to Daedalus. The illusions both get the evasion and 30 Agility, while they only benefit from the Critical Strike from Daedalus. If your opponents don't have too many AOE nukes or ways to deal with your illusions, I think this point should be considered, especially since the illusions can deal quite a bit of damage and be generally disruptive when you put Evasion and an Eye of Skadi on top of them. Indeed, this argument is probably better suited for heroes like Naga Siren and the likes, however if we are talking about lategame and with the HP buffer Eye of Skadi provides, it may be worth considering even in the case of a Sniper.

After all, they're both great choices, and the choice is situational. However, I think you should consider illusions when choosing, especially if you have other ways to produce some of them on top of a Manta (for example, an allied Shadow Demon or Morphling).

EDIT: Another reason to prefer Butterfly over Daedalus is the damage against structures. Critical Strike won't help either you or your illusion in siege situations, while every offensive stat of Butterfly work; also, your Butterfly-boosted illusions have a much easier time being useful against structures than against heroes: the target does not move, you have huge range, and you can get uphill vision with Shrapnel to siege more effectively.

bunyaCloven already gave a nice in-depth-math answer but there is one big rule you always need to remember when playing MOBA and especially on DotA 2: Item Choice is ALWAYS situational! meaning you may ask for the better item but you will always receive the answer that I depends on the situation.

If you face a heavy auto-attacking team you would almost always try to get butterfly ASAP but it wouldn't be necessary if there'd be 3 of 5 stunners. Than first choice is BKB and then damage...you really need to make the items fit the enemies line-up as well as your playstyle!

try to keep it in mind :) & good luck further on.

Above answers address your question, but just for the sake of argument, if you think logically, being a sniper you would ideally be standing a little far from the gank.

If you position yourself ideally, it will be very hard for the enemy hero to come to you. On top of that, you have headshots and slow from skadi, which will make the enemy approach even slow. Hence there will be a very little chance that the enemy hero will actually get to hit you or do substantial damage.

Therefore going for butterfly(people go butterfly mainly for evasion) will provide less advantage than daedalus. Having Daedalus will improve the chances of finishing enemies before they reach you.

Ofcourse I am not accounting for invisible or blink heroes. You might have to get butterfly in that case.

And as all the other answers conclude, its all situational :)