Nannies, if paid legally, are definitely the more expensive option. You need to pay federal and state taxes, some states require worker's comp, and if they're going to drive your child you need to do something about car insurance. It's a lot of paperwork, with hefty fines for not doing it correctly. However, you get the benefit of care in your own home. No scrambling to get the kids out the door in the am, no worries if you're running late. Most nannies will watch sick kids and will work flexible hours. My sister's daycare will call social services if you are more than 15 minutes late without notifying them, and charge an enormous late pickup fee. Vomiting more than once within 24 hours, fever within 24 hours, or current "excessive" drippy noses mean you have to keep them home. My sister has missed a lot of work for various reasons. Meanwhile, our kids both had pinkeye and fevers, but our nanny came in anyway. Our last nanny worked for us for a year and a half and never took a day off. She was amazing, and if anything our new nanny is shaping up to be even better. Nannies also have more freedom to do trips. Our kids went all over the place, to the library, parks, indoor gym, hiking, playgroups, and so on.
Daycare is MUCH cheaper here, and I think especially for older kids the socialization and structure is good, IF the center and teachers are good. We're hoping to be able to move to doing daycare instead of a nanny soon, but right now our schedules are too unpredictable. We need early mornings, late evenings, and often have to work weekends and holidays.
You can also look for an in-home daycare situation. I took my older child to a lovely lady in CT. She was not licensed, but she had extensive experience with multiple daycare ages - she had just decided to stay home when her 2nd child was born. She only watched 2 additional kids at any given time, and stuck to kids around the same age as her older child. She had a nicely set up kids room, fed them healthy home cooked meals, and was flexible with her hours. I know quite a few SAHPs who watch an additional child. If you find someone you like and trust, it can be a fabulous experience, and is usually very reasonably priced. I paid a whopping $5/hour.
Whatever you decide, remember that full-time care of any kind is a temporary situation. It's expensive, but that's one thing that will decrease the older they get. I also think that excellent childcare is a worthwhile expense. You're talking about people who help shape who your child is.