Stiffness is more of an issue of stability than accuracy. Nonstiff solvers can solve stiff problems, it just takes them a long time to do so.
I would also note that since ode45 is meant to be a general-purpose solver, it uses interpolation to output extra points per step, which leads to better plots. This is controlled by the 'Refine' option, which has a value of 4 for ode45 and 1 for all other solvers. So if you want ode15s to output some extra points per step as well, just use
opts = odeset('Refine',4);
[t,y] = ode15s(@odefcn,tspan,y0,opts);