Two Analysts, One Posterior

A subscription company starts with a $\text{Beta}(2, 3)$ prior on $\theta$, the probability that a customer renews.

Analyst 1 updates sequentially:

• On Monday she observes $6$ renewals and $2$ non-renewals, and updates the $\text{Beta}(2, 3)$ prior.
• On Tuesday she takes Monday's posterior as her new prior and feeds in Tuesday's $10$ observations ($4$ renewals, $6$ non-renewals) one at a time, in a randomly shuffled order.

Analyst 2 discards the intermediate step entirely. He pools all $18$ observations and applies a single Beta–Binomial update to the original $\text{Beta}(2, 3)$ prior.

Which statement correctly describes the two analysts' final posteriors?