I've looked at Google and PubMed and was not impressed by what I found. Most "screen time" studies are primarily or exclusively TV-watching studies, and in many cases are in turn using that as a proxy for sedentary behavior in general rather than actually examining media consumption patterns. In short, they don't demonstrate that all screen time is equivalent, they just define the variable that way. That can be entirely justifiable from a study design standpoint, but also limits what the results can tell us.
The main source for recommending limitations on overall screen time for young children seems to be a set of recommendations published by the American Academy of Pediatrics [1], but they don't actually cite any research (or their citations are too well-hidden for me). The AAP recently published a release stating that new recommendations are coming soon and suggesting that the old guidelines are unnecessarily rigid and unrealistic, even to the point of explicitly stating that "The public needs to know that the Academy’s advice is science-driven, not based merely on the precautionary principle.". The top bullet point is "media is just another environment". This newer document generally advocates a nuanced approach that takes the nature of the content or activity as well as the social context of media consumption (e.g. whether parents are actively watching with the child) into account [2].
The main source for recommending limitations on overall screen time for young children seems to be a set of recommendations published by the American Academy of Pediatrics [1], but they don't actually cite any research (or their citations are too well-hidden for me). The AAP recently published a release stating that new recommendations are coming soon and suggesting that the old guidelines are unnecessarily rigid and unrealistic, even to the point of explicitly stating that "The public needs to know that the Academy’s advice is science-driven, not based merely on the precautionary principle.". The top bullet point is "media is just another environment". This newer document generally advocates a nuanced approach that takes the nature of the content or activity as well as the social context of media consumption (e.g. whether parents are actively watching with the child) into account [2].
[1]: https://www.aap.org/en-us/advocacy-and-policy/aap-health-ini...
[2]: http://www.aappublications.org/content/36/10/54.full