In Journey's End, the Doctor tells Donna that the human brain can't contain a Time Lord mind. How is it possible with the cloned Doctor, if he has a human body? Wouldn't he shortly start to experience the same side-effects?
The MetaCrisis Doctor was a mixture of Gallifreyan and Human DNA so while he may have come away with a limited lifespan, no regeneration, and only one heart, his brain was still able to manage the information consistent with being a TimeLord because he possessed Gallifreyan DNA. He will likely be comparatively a poor Gallifreyan but a superior Human, overall.
The DoctorDonna was a Human who was temporarily exposed through the Metacrisis to the INFORMATION embedded within a TimeLord's mind. However, she was incapable of maintaining access to the information because of her Human brain.
Since he would have no further contact with the TARDIS he may still possess a number of superior physical and mental characteristics consistent with Gallifreyans but the superior long-term memory may be one of the casualties of the Metacrisis Event.
The primary difference is Donna was all Human and had no chance of keeping access to the stores of amazing information available to her. If I were a betting man, I would assume it was the TARDIS which helped her be able to make sense of it at all, sufficient enough for her to use it for a time and buffered her from the worst effects of it.
Human-Time Lord Meta-Crisis is the term applied to a hybridised organism that combined the traits of a Time Lord and human. Only two have been known to exist, namely the "DoctorDonna" and the Meta-Crisis Doctor.
The DoctorDonna was an example of a human with a Time Lord consciousness. She had to be reverted to her human self; her brain could not hold a such a consciousness. The Doctor had to erase her mind of all knowledge of him. (TV: Journey's End) Despite this, Donna's latent consciousness remained half-Time Lord, protecting her when the Master turned the world into copies of himself. Apparently, it also subconsciously guided her to buy a book for her grandfather, which led the Doctor and him to Joshua Naismith. (TV: The End of Time)
The Meta-Crisis Doctor seemed to be a mixture of the two races. He did not burn up, presumably having a Time Lord brain, but only had one heart and could not regenerate. He also showed quirks of Donna Noble, the human with whom the Meta-Crisis occurred. (TV: Journey's End) -- TARDIS Wikia > Human-TimeLord Metacrisis
I suppose in the case you're referring two, the biology of a Time Lord would also be cloned, thereby enabling the cloned Doctor to contain a Time Lord's mind.
The Meta-Crisis Doctor IS the doctor's consciousness in human form. It's no different than when the Doctor put his consciousness in the fob watch. The new body is merely a "handy bio-matching receptacle" which happens to have the ability to act and move. When the doctor nearly regenerated after being shot by the dalek part of his life force was put into the energy around him and sent into the hand which was touched by Donna which created the new doctor. So when the doctor tells Donna's mom and grandfather that she took his mind into her own and it was a "time lord consciousness" it's a completely different process. Meta-crisis won't burn because he IS the doctor. It's the same consciousness. He can't be overwhelmed by new information because he already knows it all. Does that make sense?