Both the greybeards and the dragons are capable of summoning the thu'um.

Why does the Greybeards thu'um appear stronger than the dragons thu'um. When the greybeards speak, it is said that storms and lightning appear as a proof of their powers. But when dragons speak this doesn't happen. The most similar thing is when Alduin summons the meteor shower. But this shout is unique to him so it doesn't really count.

Aditionally it is said in the game that normal mortals cannot withstand the voice of the greybeards, however dragons communicate fine with other mortals. A dragons thu'um doesn't affect his normal speech unlike the other 3 greybeards.

Is the Greybeards thu'um stronger? Or is it that dragons can control it more?

The Dragon's Thu'um would most likely be stronger since a Dragon is created with it and use it as their form of speech.

Do not underestimate the Greybeards, a mere whisper from there mouth causes High Hrgothar to shake.

The problem here is that Greybeards and their thu'um were referenced in lore as far back as Morrowind at the latest, while the idea of dragons using thu'um as their form of speech is new as of Skyrim. So we've had at least three games in which to build up a written version of how awesome the Greybeards are, but our impression of dragons is tainted by gameplay limitations as soon as we encounter them. That said, are there really no texts in Skyrim that explain just how powerful and damaging a shout from a dragon could be? If true, that's a pretty interesting oversight. Regardless, the devs likely figure that we can use our imagination to say, "If the Greybeards are supposed to be able to do this, how much more awesome must a dragon be?"

Actually Alduin's 'meteor shower' is not unique to him. All it is is Storm Call level 3. The third level of that shout summons fireballs from the skies instead of lightning bolts. So the greybeards can do that too.

But yeah, good question on the shouts there, it does seem like in fact the greybeard's shouts are stronger then the dragons. Dragons can talk to mortals fine, but greybeards cant? Maybe theres some different effect with shouts coming from humanoids or mortals, then from dragons? I dunno.