Well, being I have a 2016 Aprilia RSV4 RF and a 2015 1299 S in the garage, maybe I could answer a little. I have ridden both back to back. The 1299 S is my daily rider, and the RSV4 is my wife's daily rider. Honestly, I would own either of these bikes if I had the choice. Depends on if you want to say "I own a Ducati" or not. Or if you go to a MotoGP event and want to get in to Ducati Island parking with your Ducati. There are some perks to owning a Ducati that aren't there with the Aprilia.
Which one gives you the bigger... smile?
In terms of power/performance, this totally depends on how you ride. The Aprilia is top end power. It's missing the low end grunt of the Pani, seems to bog with low RPMs. Red line on the RSV4 is 13900 (I think, it's my wife's bike), and power really comes in around 9k RPM to red line, like an on/off switch there, power seems almost instant. The Pani pulls from 5000 to red line, and you can feel the grunt all around, and power feels kinda linear across the powerband, just freaking pulls anywhere. My 2007 R1 was peak power, rocket ship above 9k RPM, like the RSV4, in fact I found their power bands very similar, but the RSV4 has a bit more punch in the middle, but riding back to back with the 1299, it's lackluster in the bottom and mid-range. But if I ride back to back with the R1, the RSV4 pulls mid-line, and top end is similar.
Sound, dead sexy for both. When we have passed people, they have said "I don't know which one I liked being passed more, the V twin or the V4." LOL
In terms of handling, proper setup suspension for either bike are great. The S has the electronic, which I wanted, and it works well, but really, it wouldn't have bothered me having standard Ohlins forks and just make adjustments on occasion.
Electronics, very similar, especially if you have a pre-2017 model, which Aprilia really upgraded a few things, but pre-2017, the 1199 beats it. Although Aprilia does have a add on module that lets you make changes to settings based upon GPS coordinates for track using your phone. Need more wheelie control in turn 4, you can turn it up for that corner only, need more TC in a corner, turn it up. Pretty trick stuff that isn't on the Ducati.
Paint. Aprilia. The paint on the 1299 is thin, I have 3 rocks chips on the nose and one on the rear of the bike, from just standard riding, and I usually lead. Not super impressed with the Ducati paint, but the RSV4, it's a nice paint job, and feels like it will hold up better, there are some edges of the paint on the RSV4 that just didn't have attention to detail (overspray), but maybe we had a Monday painter...
Everything else is a toss up. Both bikes handle well, both are similar weight, both sound great. Really, which do you like better. Ducati parts are more expensive, but seem to be available, where some aftermarket stuff for the RSV4 is harder to get.