I've done both. We are currently back in private home care and I hope we will be fortunate enough to stay right where we are.
That said, you asked for a comparison between the two:
Daycare Pros:
Wider Hours
Continuous Coverage (especially around the holidays)
More available activities
Depending on where you go, possibly more structured curriculum (learning care vs. playcare)
Cons:
More kids
More exposure to germs
Less individualized attention, tougher to communicate
Typically more expensive
Easy to solicit references by talking to parents in the parking lot at beginning/end of day to get a feel for what the place is like.
Private Care
Pros:
Individualized care
Less kids
Less exposure to germs
Depending on the type of provider, structured curriculum
Easier to communicate and establish relationship with sitter
Typically lesss expensive
Cons:
Tend to open later/close earlier
Tend to use more time off aroud holidays
Coverage is a concern in case sitter is sick/needs time off
Have to work a bit harder to vet them out.
I'd certainly check their info out on the TX Dept Family Services website. I always look for violations that are concerning. I would not consider a private sitter unless I knew them well, who isn't a licensed caregiver. First for the regulatory oversight, and second because for a person to go through everything to be licensed shows how serious they are about what they do.
There is a bit of parent radar use as well. I have a rather exhaustive set of interview questions for any prospective sitter/childcare place as well as reference questions and if any alarms go off during that check, all bets are off. Message me and I'll send if you are interested.
At daycares, I always look for cleanliness, do the kids look healthy, how the kids interact with the teachers, whether my gut felt comfortable talking to the teachers/director, and what the parent feedback in the parking lot is.
Same thing with private sitters although I had to rely more on references that the sitter picked out...so I put more weight on my parent radar when interviewing everyone.
Hope that helps. Good luck!