I'm flying to Rio may next year, 6 nights (that's the only change to get that promo fare).
Is it worth to fly to iguacu for 2 days? Just to see the brazilian side? Or better save money for day trips from rio?

How badly do you want to see the falls? The Brazilian side only takes a couple of hours btw.

One could easily spend that entire time in Rio.

Guess it depends on how much you like waterfalls. I thought the falls were magnificent, easily outclassing Niagara, but I also think you should see both sides. Not difficult, use buses or taxis, but you might have a visa issue.

For Argentina (for US passport holders), It's not a "visa"; it's a reciprocity fee, payable online.

The issue is flying half a day to spend a couple of hours on the Brazilian side followed by another half day to fly back to Rio, out of a total of only 6 nights,

I would suggest arranging a connecting flight and flying from Rio to Iguazu on arrival. I think I spent rather more than two hours on the Brazilian side, but I agree that the Argentinian takes longer. Allowing for jet lag, I would spend two nights in the area. Of course, I thought the scenery in South America easily outshone the cities, YMMV.

Except that for Rio, the city IS the "scenery" (or the scenery is the city), that which makes Rio unique. Rio's natural areas are a large part of its touristic attraction, and most foreign tourists see more Brazilian natural beauty in Rio than in travel to other parts of the country. When foreign tourists do travel to scenic natural areas of Brazil, those visited tend to be the ones swarmed by other foreign tourists (sadly IMO).