Which rate is faster: one step with Ea or two steps each with Ea/2?
Instead of looking at $\mathrm{d}[\ce{P}]/\mathrm{d}t$ against time $t$, a better idea might be to plot $[\ce{P}]_t$ against $t$, which you already did. By eyeballing the graphs I'm fairly sure that $[\ce{P}]_t$ in case 2 is always below $[\ce{P}]_t$ in case 1.

In org chem, people probably aren't too interested in what the absolute rate of the reaction at time $t$ is, they are probably more interested in how long the reaction will take to run. Because of the maths, the reaction will never hit 100%, so you can't use that as a benchmark, but you can use e.g. 95% complete (i.e. $[\ce{P}]_t = 0.95$) as a benchmark.