We study the effect of matrix chain molecular weight M-w and concentration c on the electrophoretic mobility mu of large linear and star-like, branched DNA in polymer solutions. Polyethylene oxide (PEO) with narrow molecular weight distributions form the main focus of this study. For PEO concentrations ranging from one half the overlap concentration, c*, to 3c*, the effective drag coefficient, zeta drop mu(0)/mu - 1, satisfies the following approximate scaling relationship, zeta similar to cM(W)(0.7). Here, mu(0) is the electrophoretic mobility W in free solution. While the concentration dependence is consistent with predictions from the transient entanglement coupling (TEC) model, the molecular weight dependence is significantly weaker. Although a similar dependence of mobility on M-w can be predicted when nonentangling collisions are the dominant source of drag, a model based on these collisions alone cannot reproduce the experimental observations. We also find that the architecture of large DNA does not affect either the concentration dependence or molecular weight dependence of the electrophoretic mobility.