The PL has some "evidence" that what they allege has actually happened. We know that from the leaked emails, but we also have to assume they have more "evidence", for more years, from their investigation.
The problem for the club is to show that something that didn't happen, didn't happen. The way they did that at CAS was to get an independent auditor to look at payments from ADUG and show none went to Etihad. It's a start, but it's not wholly convincing (the money could have come from another ADUG company, for example, or be routed through other companies or come from Mansour's personal accounts). By the way, this is why control of access to external information is so important. The club can now control, to a great degree, the information it provides to the panel, and in what format they present it. Anyway, together with the witness statements that it didn't happen, including statements from Etihad that they didn't receive any money from ADUG or Mansour, which CAS found compelling, it was enough to sway the majority of the panel, with comfortable satisfaction, in favour of the club's position. The audit report(s) this time will be different and the witness statements presumably also, to cover the greater number, and specificities, of the 115 allegations. So much for the club's problem.
The PL's problem is that their "evidence" is entirely circumstantial, as was UEFA's, and they have the burden of proof to show that the alleged behaviours, on the balance of probability with a high degree of cogency, actually took place. UEFA couldn't, and I very much doubt the PL will be able to, either. Certainly not on the most serious charges.