Criminal charges definitely require a higher level of proof but for these examples I think that a conviction is more certain.
In the file sharing case consider what they need to prove: they need to establish that a file not only looks like it contains infringing material (e.g. a copy of a movie) but that it actually does. They need to prove that the defendant willfully downloaded the file at a particular point with the intention of violating copyright, which requires identifying the user via IP and establishing that the particular defendant's computer was using that IP at the time the transfer took place. In many such cases the defendant's computer has not been seized and can't be used as evidence.
Now look at the case for a LOIC DDoS prosecution. On the one hand you have the evidence from the targeted site, which consists of server logs, router logs, and ISP traffic logs which (as above) can tie the defendant to the DoS incident. On top of that you likely have IRC logs of the organization of the DoS, these even more uniquely identify the defendant since they include information unlikely to be duplicated on another user's computer. Also, because this is a felony criminal case it's likely that the defendant's computer's have been seized. That provides an additional depth of evidence, such as if the computer's have LOIC installed, if they still have local IRC logs which can be tied together with other evidence, etc. Additionally, a DoS attack has an unusual signature in that it represents a lot of upstream traffic from a client, there will be evidence of that signature in the ISP's logs and on the client computer itself (cached dns entries, up/down traffic data, etc.)
On the whole I think the DoS case is likely much easier to prosecute than the file sharing case, despite the higher burden of proof.
They need to prove that the defendant willfully downloaded the file at a particular point with the intention of violating copyright
No, all that is needed to prove is "making available". Even if you ripped your legally purchased CDs, and then installed Kazaa, which then detected the mp3s on your computer, and then began sharing them, without your knowledge, you would still be liable.
Infringement really has nothing to do with intent unless you are attempting to argue fair-use.
In the file sharing case consider what they need to prove: they need to establish that a file not only looks like it contains infringing material (e.g. a copy of a movie) but that it actually does. They need to prove that the defendant willfully downloaded the file at a particular point with the intention of violating copyright, which requires identifying the user via IP and establishing that the particular defendant's computer was using that IP at the time the transfer took place. In many such cases the defendant's computer has not been seized and can't be used as evidence.
Now look at the case for a LOIC DDoS prosecution. On the one hand you have the evidence from the targeted site, which consists of server logs, router logs, and ISP traffic logs which (as above) can tie the defendant to the DoS incident. On top of that you likely have IRC logs of the organization of the DoS, these even more uniquely identify the defendant since they include information unlikely to be duplicated on another user's computer. Also, because this is a felony criminal case it's likely that the defendant's computer's have been seized. That provides an additional depth of evidence, such as if the computer's have LOIC installed, if they still have local IRC logs which can be tied together with other evidence, etc. Additionally, a DoS attack has an unusual signature in that it represents a lot of upstream traffic from a client, there will be evidence of that signature in the ISP's logs and on the client computer itself (cached dns entries, up/down traffic data, etc.)
On the whole I think the DoS case is likely much easier to prosecute than the file sharing case, despite the higher burden of proof.