For me the most important factors to consider would be:
- housing costs: locals are on waiting lists for years before they find decent and affordable housing to rent in the center of either city; probably your only option is to contact a private agency. Amsterdam may be more extreme in this respect than Leiden, but the latter being a student town with many people in their 20s and early 30s looking for a studio or 2-3 bedroom appartment, there's a lot of competition for that particular type of housing too. If you cannot afford to live in the city center, you're probably better off living in Leiden because that town is smaller and you can get everywhere by bicycle in no more than, say, 15 minutes (residential areas are the same everywhere, and I don't really see the added value of living in a dull appartment block in Amsterdam as compared to a similarly dull appartment block in Leiden).
- commuting time: if you can afford to live in the center of Amsterdam and your company is within walking distance or a short bus ride from Leiden Centraal train station, it wouldn't be a problem at all to get to/from work by public transport; you'd be crazy to drive a car in the center of either town, and the lack of parking space would be a major headache. If, however, you end up living outside the town center and you can park your car at work, it may be faster to travel by car - Pijlmans nailed it in #4.
A few random thoughts:
- I've been living in Leiden for about 15 years now and although I generally like cities, have never considered moving to Amsterdam. Leiden offers about everything I need - a beautiful historic center, several museums, a good selection of shops, many decent restaurants (and often better value than what you find in central Amsterdam), lively pubs, a theater, severals cinemas and excellent transport connections to every major town in the Randstad area. What Leiden does not have, however, is bus loads of tourists, foreign scum on stag dos, coffee shops on every street and tacky souvenir shops ;-)
There may be a bit more going on in Amsterdam than in Leiden in the way of cultural events and festivals (though "3 oktober" gets pretty wild), and when I want to go to a concert or a football game or just sample a few beers at one of the specialized beer cafes, I head for Amsterdam, but other than that, Leiden is perfect for me.
- As said above, Amsterdam may be bigger than Leiden, but it still has a bit of a small-town feel; if you're looking for a city that feels like a big city in the North American sense, Rotterdam would be your best option.
Housing agencies for Leiden include:
Kamernet (http://kamernet.nl/kamer-Leiden-tot1200/?minOpp=6&sortering=0&asAlert=0&UserGSM=&maxSMS=&checkSMSAlert=0)
Living Today (http://www.livingtoday.nl/english)
Direct Wonen (http://www.directwonen.nl/default.aspx?setlocaleid=1033)
Buro Hogeland (http://www.burohogeland.nl/overzicht.aspx)
Kamernet and Hogeland are in Dutch only, but the links I gave will list the options for Leiden; I'm afraid you will have to brush up your language skills a bit or use Google Translate to read the details. Warning: always have a look at the room first before handing over your money, and be prepared to pay at least one month rent on commission.