I think it's fair to say that a strict level of proof has to be established beyond a reasonable doubt that the murder is planned and deliberate. I don't think the jurors in this country have a great deal of difficulty understanding that concept.
As a matter of fact, I think we're moving to standard jury charges throughout the country that judges would give in relation to these. I don't believe there seems to be any information or statistic that jurors are having difficulty interpreting what “planned” and ”deliberate” mean and what the difference between first- and second degree-murder is. I think that through judicial institutes, etc., judges have really gone out of their way to make them standard.
However, in response to your question, I think it's fair to say there is a higher onus on proving planning and deliberation because of the maximum punishment.