The number of discovered exoplanets now exceeds 5500, allowing statistical analyses of planetary systems. Multi-planet systems are mini-laboratories of planet formation and evolution, and analysing their system architectures can help us to constrain the physics of these processes. Recent works have found evidence of significant intrasystem uniformity in planet properties such as radius, mass, and orbital spacing, collectively termed `peas in a pod' trends. In particular, correlations in radius and mass have been interpreted as implying uniformity in planet bulk density and composition within a system. However, the samples used to assess trends in mass tend to be small and biased. In this paper, we re-evaluate correlations in planet properties in a large sample of systems with at least two planets for which mass and radius have been directly measured, and therefore bulk density can be calculated. Our sample was assembled using the most up-to-date exoplanet catalogue data, and we compute the relevant statistics while using a procedure to 'weight' the data points according to measurement precision. We find a moderate correlation in radius and a weak correlation in the densities of adjacent planets. However, masses of neighbouring planets show no overall correlation in our main sample and a weak correlation among pairs of planets similar in size or pairs restricted to M_p_<100M_{Earth}_, R_p_<10R_{Earth}_. Similarly, we show that the intrasystem dispersion in radius is typically less than that in mass and density. We identify ranges in stellar host properties that correlate with stronger uniformity in pairs of adjacent planets: low T_{eff} for planet masses, and low metallicity and old age for planet densities. Furthermore, we explore whether peas in a pod trends extend into planet compositions or interior structures. For small neighbouring planets with similar radii, we show that their masses and interior structures are often disparate, indicating that even within the same system, similarity in radii is not necessarily a good proxy for similarity in composition or the physical nature of the planets.