Why not buy yourself both ? Resistance bands are an inexpensive way to strength train at home or on the road. You can find them at any Walmart, Target, Sears or even TJ Maxx for under $10. You could probably get a set of three for around $15. Hand weights are fairly inexpensive. they start getting really pricey for the higher weights above 20 pounds.
My rule of thumb for picking hand weights, get your bag. The one you carry with all your stuff, not your purse. Weigh that bag. How heavy is that bag ? I did a survey and found that many women carry bags that routinely weigh 8-10 pounds. So, if you lug around a big heavy bag, you can handle 8-10 pound hand weights.
Using those little girlie weights will not give you dainty muscles. If you want to see some definition, don't be afraid to lift a heavy weight. You will NOT get bulky if you lift something heavy. that is a misconception. Women don't bulk up picking up heavy weights.
If you're new to using resistance bands, I highly recommend you join SERGEANTMAJORs resistance band team. he's got a ton of basic and advanced workouts using bands posted. www.sparkpeople.com/myspark/groups_individ