Perhaps it depends on how big your luggage is. There's otherwise no need to stay near the Train station in either city. Neither is a "run-down" area, as are many European train station areas. But neither has much charm. I personally would be glad to walk to the museum area in Amsterdam from the train station, but many people would say it is too far. If you're going to buy a tram/bus pass, it doesn't matter where you stay. Most posters here place cost above other hotel criteria.
If you were staying longer, there are many good daytrips on the train from Amsterdam. But you will have two or three very full days just in Amsterdam. It is a large city, and you would do well to get a local transit pass, just to cover more ground. Have you reserved/bought your Anne Frank house ticket yet? This is urgent.
Your actual question is confusing. Are you chosing which city to have more nights in? The character of the train station area is a poor criterion to make such a choice. I like Leiden a lot, but there is much more to see in Amsterdam. In fact, Leiden can be skimmed over nicely in a day trip from Amsterdam, if you get a comfortable hotel there with a good price. Then you don't have to waste half a day picking up and moving. Don't forget that rooms are not ready for occupancy in the morning.