The resulting response is going to have a lot to do with your room and how you set up your new sub.
If I were buying one right now for $1000 or less, I'd go with one of SVS's PC-Plus line. In particular, I'd get the 16-46 PC-Plus. You can view the measured frequency response on their product page
here. The 20-39 also looks to have a very flat response. They have a new model coming out (so those two are on clearance) with a new woofer and amp called the PC12-Plus. The response is shown on the product page
here. That new model is on pre-order, so there aren't customer reviews of it. I have a PC13-Ultra, so I'd lean towards the 16-46, but I'd e-mail SVS and discuss the differences between it and the new model.
That's what I would buy, but that's heavily influenced by the fact that I own an SVS, really like it, and really like my experience with the company. I don't have much experience with other recent subwoofers.