I have a d800 which I use extensively for stills and video.
I'm considering a D3300 as a second camera for video shoots, because is cheap and has 1080 50/60p.
I'm trying to find a review for its video performance, but I cannot.
Does anybody have a clue of any shortcomings or how it compares video wise to d5300?

I know there are a few enthusiastic users of nikon d5300 and most likely d3300 so you could get some useful info there as well, from what I have read both perform about equally with the only difference in some functionality, if you google d5300 vs d3300 there are plenty of articles and videos talking about what is different.

I have read everything. For 200€ you get wifi articulate screen and better AF. But nowhere I have found a real world footage comparison.

You can read a review on dpreview and also check this link out Nikon D5300 vs D3300 - 5 Key Differences - YouTube

To summarize both the d3300 and d5300 use the same sensor, and have the same video features/performance. The main differences are the lcd, af system, and Wi-Fi.