It all depends on what language you are programming in. GML, C++, C# or Java. Because it makes a lot of difference.I don't know how it would make a difference, since this sounds more like a graphical hurdle.
Actually it does matter. For C++, C# and Java, I would also say create a particle emitter. However in this case for GML I have to differ. GameMaker Pro has some particle system effects that you can use, but these are Pro only. For Lite I suggest you just make a big sprite containing the explosion and have a single object draw it.
If you are going to make an object for every little particle, you can get a dozen objects at once, which Game Maker treats as regular objects, like the player, MC, NPC and obstacles. And when you get a barrage of explosions that the number of objects can increase rapidly, even if their life time is limited. This increase in objects can seriously lag your game. Okay any particle emitter already puts a strain on the game anyway, but creating objects is even worse.
But then again you could create only one object and then draw the various particles at their right places for each frame. This requires some serious calculations or a very big switch statement.