It comes down to a question of whether your finances can handle two mortgage payments (assuming you have a mortgage on both homes). Your lender will tell you whether you can actually qualify for a mortgage to construct your new home. So, ultimately, this is a personal preference. Do you want the new home enough to float two loans plus utilities, maintenance, insurance, and taxes? Make sure you keep enough money available to repair your current home so you can sell it easily (and consider that something very costly may be wrong with your house without your knowledge). Also consider the possibility that if you lost significant income through job loss, could you support both homes? If you have a financial advisor, you should run this by him/her.
You selling status will change slightly: once you move to your new home and if your current home is still on the market, then you'll no longer have your furniture in the home. As a bonus, if your furniture actually doesn't fit your current home, then it will show better! It will also be available to be shown at any time, opening your home up to slightly more prospects...those who request to see it on a moments notice. And, you'll no longer need to upset your daily routine to keep the house in show-ready condition!
Finally, you might get lower offers on your home. People might perceive that you have a stronger desire to sell at a loss when you leave the home vacant. But, you can decline these offers, and if they love the house enough anyway, they'll come back to a better price level. So, this could be a positive and a negative effect, just depending on the buyer.
I hope that helps!