The effect of copolymer compatibilizer on the rheology of polymer blends, as well as four-roll mill studies of the effect of compatibilizer on coalescence of a pair of drops is reported, with a focus on so-called symmetric systems with equal bulk fluid viscosities and a copolymer with equal block molecular weights. The primary experimental system consists of polybutadiene (PBd) and polydimethylsiloxane (PDMS) as the bulk polymers, with a “symmetric” PBd-COO-NH3+-PDMS copolymer with equal molecular weights on each block as compatibilizer. Motivated by earlier work of Martin and Velankar, we performed experiments with PBd as the drop phase and PDMS as the matrix phase and also experiments with the roles of these two materials reversed. The rheological properties for the inverted blends are distinct, as also shown by Martin and Velkankar, and the symmetric copolymer is also shown to have an asymmetric effect in the suppression of drop coalescence when we reverse the materials of drop phase and matrix phase. Two mechanisms can lead to the suppression of drop coalescence: immobilization of the interface due to Marangoni stress leading to slow drainage of the thin film between colliding drops, and steric hindrance of film thinning. At the same copolymer concentrations, we find that the Marangoni effect is the same independent of which fluid is the drop. However, the steric effect arises from the adsorbed copolymer forming an extended polymer brush configuration on the outside of the drop, and for our present system this contribution depends on whether PDMS or PBd is the continuous phase. In general, the conformation and thickness of a polymer brush depends not only on the copolymer concentration on the interface but also the MW of the copolymer block and the molecular weight of the corresponding bulk homopolymer. With PBd drops and PDMS as the continuous phase, the experimental evidence suggests that the brush layer formed by the PDMS block of the copolymer is too thin even at very high copolymer concentrations to produce a steric effect on coalescence. On the other hand, with PDMS drops and PBd as the continuous phase, the brush thickness external to the drop is sufficiently large at high copolymer concentrations (Γ > Γc), to totally prohibit drop coalescence in the four-roll mill. These studies suggest that it is the presence or absence of an extended brush, along with the effect on average drop size that is responsible for the differences in the rheological properties of the inverted blends.