After Slughorn's memory had finally been successfully retrieved, Dumbledore told us that he'd started to suspect the existence of Voldemort's Horcruxes after Harry recounted the happenings in the Chamber of Secrets. He highly doubted that a mere memory could have independent thought, the ability to possess people and consume their life-force.

The Locket Horcrux was clearly just as dangerous, it just didn't have as much opportunities to create damage. The locket could clearly suck something out of the Trio, Harry was unable to cast a corporeal Patronus after wearing it for a long period of time. The locket also contributed to Ron's mood swings, and showed him a cinematic representation of his worst fears. And let's not forget the attempted strangulation.

This shows us that turning the Diary into a Pensieve or a portrait equivalent would not have been enough to create an object that could open the CoS, and decide that Harry Potter was a bigger priority than Slytherin's noble quest.

But yet, we have moving pictures who can occasionally react to the environment or the feelings in the captured moment. We have talking portraits who party and seem at least somewhat intelligent conversationalist. The Priori incantatem echos helped Harry in the graveyard, and they came up with a successful escape plan. And let's not forget the Sorting Hat.

So what's the difference between Memory-Riddle and Dumbledore's Portrait, aside from the obvious?

 

Rowling herself tried to answer this one at her website...

This explanation mostly works for me, I guess: a Horcrux, being an actual bit of soul, would ultimately be a lot more flexible. It still leaves questions open about Dumbledore's portrait, which seemed to be rather more involved in scheming than we've seen from other portraits. But maybe it just seems more clever than a normal portrait because Dumbledore was more clever than a normal wizard?

 

It was because he died very recently and a lot of events, especially regarding the war, were really relevant to his interests. I don't think you can say it for any other portrait, they simply had no reason to care.

 

My biggest problem with Rowling's answer is that she uses a Portrait that seems more of an exception to the rule as an example.

The Fat Lady and Sir Cadogan are much better suited for the task, IMO.