Construct would probably be better for getting started quickly and scaling that to slightly more complete games, however processing also gives VERY easy to understand networking, Internet and serial functions. I'd rather use processing as I'd know that I'd have so much more choice.
But are those really vital necessities for a single-player platformer game? Construct's online capabilities are pretty much highly limited at the moment, but if you want to do something simple like online scoreboard for your game it's easy to do with Construct.
As I said, Processing doesn't really feel like a tool intended primarily for game development, whereas Construct is specifically that. And for game development, Construct offers very much. You can pretty much say that if it's 2D, it's completely doable in Construct. Of course you could say the same about tools like Game Maker or MMF2, but for example doing something like a bullet hell game with thousands of bullets onscreen isn't really that feasible to do with GM's or MMF2's runtime performance, whereas with Construct it is entirely possible. The engine and the tools Construct provides for 2D game development are top-notch.
The only thing you seem to market with Processing is that a) it's easy for a programming language b) it has good internet capabilities. But what else is there to it? Frankly, just these two alone aren't really all that much when it comes to game development. What makes it a good choice for game development over other alternatives?