This year (1998) you can convert Westin points to Sheraton points, though you need to convert at least 20,000 Westin points. You get 1 Sheraton point for 5 Westin points. I am planning to convert my Westin points to Sheraton at the end of the year as I figure that Sheraton points are a better value for me. You need to look at the award charts and your points in both programs to determine if you want to transfer points from one program to the other (you can also convert SCI points to Westin points). The programs themselves remain independent and you can only get points in Westin for stays at Westin and points in Sheraton for stays at Sheraton.
BTW if you want to maximize your SCI points you should check out the Sheraton Optima card issued by American Express. Membership Rewards gets a lot of press, but the no fee Sheraton Optima gets my vote for the most underrated credit card.