Is the combined amount of recordings on both your HWS's MORE than can fit on a single H3 HDD of 2TB? If you are both over 50% on your HWS's, then you will have to leave some recordings behind, unless you want to transfer the overfill onto an external HDD.
Also, unless they are shipping the H3 to you ahead of the install day, you most likely won't have time to perform the RJ45 port transfer--of TWO boxes--because the installers take the boxes when they finish the install. Or the installer is ready to connect your new H3, but you are still transferring and now the tech is being inconvenienced, and if he's a contractor, he is really gonna be unhappy because he either has a next install to get to or he just wants to go home at the end of a long day, even if you arrange to pay the shipping charges and send the old boxes to Dish within the grace period.
FWIW, I would only do RJ45 transfer if the H3 is a replacement RMA that already has a pre-paid postage from Dish. This gives me hours (or days) to do the transfer. However, using the external HDD for archive/backup is really the preferred way for me because I can still keep the recordings that aren't going to fit on the internal anyway. For upgrades, I've always transferred to HDD, and then transferred the recordings from HDD to the new box via USB. Works very well.