There are a number of differences; you might want to read "The Designer's Guide to Spice & Spectre."

Spectre (and other commercial products) converge better because professional programmers (rather than grad students) make sure the derivatives are computed and stamped properly for Newton's method.

Ken likes to make a big deal about Spectre being the only simulator he knows of that actually verifies that Kirchoff's Current Law is satisfied at each node; Spice looks only at the change in the residual (if delta-v and delta-i are small after some number of iterations, then usually i=0, but Spice doesn't actually compute i).

-Geoffrey