This really depends on what's important to you. Here are some things to consider.
Lifestyle - Do you like to tinker on your home? Have projects to do? Paint? Fix things up? Or, would you prefer to spend your time relaxing? Entertaining? Participating in sports? Leisure time?
Savings - Do you have money saved up for repairs? Warranty? Trade service call fees? Your portion of estimated charges? Items not covered under warranty? Here is the website for American Homeshield which is a popular home warranty company: http://www.ahswarranty.com/homeowners/faqs.jsp#basic-warranty.
With a new home, the home is covered "bumper to bumper" for the first year as long as you do the required maintenance - change filters, etc. Then, the 2nd year is quite often everything behind the walls like the plumbing, electrical, HVAC, and wiring. The roof will usually have 20-30 year warranty depending on the builder. Then, each component of the home will have it's own warranty like the A/C condenser unit, appliances, foundation, structure, patio/sidewalk//porch, windows, etc. There is no fee for the repair of these items with the builder's warranty even if several contractors are required to fix the job.
What's important to you in a lot? Is that a major consideration for you? Or, not really? Do you want something that will let the morning sun in the breakfast area? Do you want a big back yard where you can have b-b-ques? Do you want a gentle slope? Do you want a high slope at the back so you can put in a garden back there and put in some gardening logs to separate the yard? Is a pool important to you?
What about price point? It looks like you are in N. Richland Hills. Is that where you plan on buying? That will help dictate new or pre-owned, too. What will be available in your price point.
Do you like design selections already being made for you? Do you like to walk in and see the finished home? Complete with custom paint colors on the wall, wood floors and intercom systems? Or, would you prefer to make your own design selections and make your own mark on the home? Builders typically do have completed homes, but they will not have as much character, let's say, as pre-owned homes. They will typically be finished out in neutral colors to appeal to as many people as possible. Pre-owned homes are going to reflect the personal tastes of that homeowner. Builders always have some sort of incentive package going on that you can choose to put options into your new home or take some off the price. Lots of times, you can include items like blinds, garage door opener and refrigerator... again depending on price point. Could be Viking appliances, fireplace for your outdoor living space and Klipsch audio equipment for your media room.
Community - what type of community would you like to live in? Do you like to live in an older, established neighborhood with big trees and people who've typically lived there a while? Usually, there will be more grocery stores, dining, movies, and other conveniences around in this type area. You won't use as much gas going from place to place. It could possibly be closer to your work. Or, would you prefer to move in somewhere where it's new and you're just starting out in the area the same as everyone else? The higher the price point, the closer the community will be to a more developed area typically. For example, if you are looking at the $150k range, this is going to be further on the outskirts of town than if you are looking in the $450k range.
Resale value - you want to make sure you are getting the best assistance here you can. You don't want to buy at the top or bottom end of any neighborhood. Let's say if you were to suddenly get transferred in 2 years and need to sell your home, you want to make sure you can get out of it and won't lose money. You need someone who knows the area, the comps, what the trends are, and who can negotiate confidently on your behalf.
Energy Efficiency - newer homes are going to be more energy efficient. 13 SEER A/C is the current standard. You can think of a SEER rating like miles per gallon on your car. With a 13 SEER, this is going to save you about 60% on your utility bills. They will have the low-e windows that will keep your home cooler in the summer, warmer in the winter and help fade your furniture less. Some builders are offering PEX plumbing which will expand and contract unlike copper and has a 25 year transferrable warranty. More info here: http://www.zurnpex.com/Default.aspx?tabid=198 Some builders are building Green Built North Texas homes now which is where the trend is going and all homes will be mandated to be built to this code in about 5 years or so according to experts. More info on GBNT Builders: http://www.greenbuiltnorthtexas.com/#Participating_Builder_Members
Hope this helps,