Why the different effects when Sirius Black appears in a fireplace?

I'd stick with what System Down wrote in the comments: different directors. I have at least two reasons for that.

First, there is no mention of the difference in the books. He always appears in the flame. Here is what it says in the "Goblet of Fire":

The room was in semidarkness; the flames were the only source of light. Nearby, on a table, the Support Cedric Diggory! badges the Creeveys had been trying to improve were glinting in the firelight. They now read POTTER REALLY STINKS. Harry looked back into the flames, and jumped. Sirius's head was sitting in the fire. If Harry hadn't seen Mr. Diggory do exactly this back in the Weasleys' kitchen, it would have scared him out of his wits.

So, there was a fire then, as it was in the "Order of the phoenix". The first time:

She gasped, gazing at the fire; Ron dropped his quill. There in the middle of the dancing flames sat Sirius's head, long dark hair falling around his grinning face.

And the second time:

Harry whipped round. Sirius' untidy dark head was sitting in the fire again.

My second reason is that this is not the only change. For example, the pensive started levitating between two movies:

Also, professor Flitwick went under some serious (no pun intended :-)) plastic surgery:

As did Tom (the barman from the Leaky Cauldron):

Or Dobby, whose changes are a bit more subtle, but nevertheless they are there. Or Dumbledore, when the actor was changed in the third movie (tying his beard was, IMO, really an unnecessary change).

We could go on like this for quite a while, but I think you get my drift.

Oh, and by the way, I like the embers effect more, but the fiery one is more consistent with the book.

Because the medium is different.

It's clear that the spell used by Sirius Black is Floo Network's Head-only transport. But the medium for both the instances are different. In Harry Potter and the Goblet of Fire, when Sirius Black talks to Harry there is only coal present in the fireplace. But in Harry Potter and the Order of the Phoenix, when Sirius talks to Harry there is also flame there. So his appearance looks different all because of the condition of the fireplace.

This is not a canonical answer but my conclusion from watching the scene.

Because the films had different directors who probably had different ideas for how the effect should look and/or be achieved.

It's different because the effects budget was allocated differently and probably handled by a different effects team. The embers effect is significantly more complicated and refined, which means expensive and relatively difficult. The flame version is a comparatively cheap and easy solution, it looked to be primarily compositing.