Oxford's harder to get in to for this subject (97% v 92%) according to The Complete University Guide so I guess Oxford's a bit better for it, although Oxford's research quality for it is only 1% above Cambridge. LSE's got both the hardest entry requirements (99%, unless you count St Andrews for this which I don't as the average A Level entrant at St Andrews only has AAB) and research quality (tied with Edinburgh) for it.
Other places not yet mentioned that are in the top 10 for research in Psychology are Cardiff, Loughborough, York, and Glasgow.