We are thinking about moving a server with many websites to http2. Now one concerns was that if you use http2 and download all ressources parallel that it could take longer for the browser to begin with painting / rendering the page as with only http since it is waiting for all ressources to be downloaded instead of just beginning with what is already there and continue to repaint stuff as it gets downloaded.
I think this is wrong but i found no article or good explaining so i could prove it to the ones that think this could be the case.
The browser will paint when it has the resources needed to paint and this will mostly not change under HTTP/2.
I am not sure why you think a browser would wait to download all the resources under HTTP/2 but not under HTTP/1.1?
Certain resources (e.g. CSS and Javascript unless set with async attribute) are render blocking and they must be downloaded before the initial paint will happen. In theory HTTP/2 is faster for multiple downloads so all that should happen if you move to HTTP/2 is these will download sooner and so it will paint earlier.
Now the limited number of connections that browsers used under HTTP/1.1 (typically 6-8) created a natural queuing mechanism and the browser had to prioritize these critical resources over non-critical resources like images and send them first. With HTTP/2 there is a much higher limit (typically 100-120 parallel downloads depending on the server), so the browser no longer prioritizes and there is a concern that if all the resources are downloaded in parallel then they could slow each other down. For example downloading 50 large print-quality images will use up a lot of bandwidth and might make a more critical CSS resource downloading at the same time take longer to download. In fact some early movers to HTTP/2 saw this scenario.
This is addressed with prioritization and dependencies in HTTP/2 - where the server can send some resource types (e.g. CSS, JavaScript) with a higher priority than others (e.g. images) rather than send everything with same priority. So even though all 51 resources are in flight at the same time the CSS data should be sent first, with the images after. The client can also suggest a prioritization but it's the server that ultimately decides. This does depend on the server implementation to have a good prioritization strategy so it is good to test before switching over.
The other thing worth bearing in mind is that how to measure this changes under HTTP/2. If a low priority image is queued for 4 seconds under HTTP/1 waiting for one of the limited number of HTTP/1 connections to become free and then downloads in 2 seconds you may have previously measured that as a 2 second download time (which is technically not correct as you weren't including the queuing time so it was actually 6 seconds). So if this shows as the 5 seconds under HTTP/2 as it is sent immediately you may think it is 3 seconds slower when in fact it's a full second faster. Just something to be aware of when analysis the impact of any move to HTTP/2. It's much better to look at the overall key metrics (first paint, document complete...etc.) rather than individual requests when measuring the impact because of this.
Incidentally this is a very interesting topic that goes beyond what can reasonably be expected to be covered in a StackOverflow answer. It's a shameless plug, but I cover a lot of this in a book I am writing on the topic if interested in finding out more on this.