We have studied the effect of branching on the solution phase behavior of branched homopolymers using grand canonical Monte Carlo (GCMC) simulations in conjunction with multihistogram. reweighting and finite-size scaling analysis. The critical temperature (T-c) and the Theta temperature (Theta) decrease as polymer branching is increased, but the drop in Theta is less pronounced than that of T-c.. The critical volume fraction (phi(c)) rises with the degree of branching. Branched polymers are found to obey the Shultz-Flory relationship and exhibit a power-law behavior in Theta(c) vs chain length, with similar scaling exponents as those for their linear counterparts. Comparisons of the GCMC results are made to results of the lattice cluster theory (LCT). It is observed that the LCT significantly underestimates the impact of polymer branching on the critical behavior of polymers. We speculate this discrepancy between the two formulations to be due to an inadequate representation of the variation of polymer conformations with branching and neglect of fluctuations in the LCT theory.