Hi IIIIIIIIIIIII,
First off, a 6680/Q47 is a strong Score, so it could be enough to get you into your first-choice School. As such, a retest might not be necessary. Depending on the Schools that you plan to apply to, you would likely find it beneficial to speak with an Admissions Expert about your overall profile and plans. There's a Forum full of those Experts here:
https://gmatclub.com/forum/ask-admissio ... tants-124/ While it's possible that taking the GMAT at a Test Center (relative to where you took your practice CATs/mocks) may have impacted your performance, you have to be careful about assuming that that was the only factor. Before you rush back in to retest (with the At-home GMAT), there are a couple of immediate things to consider:
First, the 'format' of the At-home Test is fixed (Quant, then Verbal - with no break in-between, then an optional 5-minute break, then IR). Having to take Quant and Verbal in one sitting is challenging for most Test Takers (especially if you've been taking your CATs with an 8-minute break between sections).
Second, the process of taking (and reviewing) a CAT requires a significant amount of energy and effort - and takes time to 'recover' from. This is one of the reasons why you typically shouldn't take more than 1 CAT per week - and your last CAT should be taken about 1 week before Test Day. Since you just took the Official GMAT, you might not be at your 'best' for another Exam until at least another few days have passed.
You might also choose to purchase the Enhanced Score Report. While the ESR doesn’t provide a lot of information, there are usually a few data points that we can use to define what went wrong on Test Day (and what you should work on to score higher). If you purchase the ESR, then I'll be happy to analyze it for you.
GMAT assassins aren't born, they're made,
Rich