If you love your e-ring as it is, why not stay with it and use the money for a dream trip or something around the house, or anything else you have always wanted? Or if money is no concern, but you're sentimentally attached to the original ring, you could have both and switch off or wear one on your right hand!
This. I agree. If money is no object, get the emerald cut but keep your original. If you don't love the emerald cut as much as the round, then wear the emerald on your right hand, or wear it on fancy-dinner night with a fabulous dress.
If money IS an object, then I would suggest keeping the money for something else altogether like a romantic trip. Or, like was also previously mentioned, spend that money on a different eternity band. The one you have looks a little tight and maybe smaller in scale than the engagement ring and could maybe be a smidge bigger and looser (although that might just be the way it looks in the photo. Maybe it fits perfectly irl, I'm not sure).
If you are planning on funding the purchase of the new ring by selling the original or using it as a trade-in, then I would say, do NOT get the emerald cut. Keep what you have. You love it, it fits well, isn't too small or too large, and has emotional value. If you regret it, you can't get it back. On the other hand, if after a few months, you find yourself so focused on the emerald cut that you are starting to fall out of love with your original ring, you can always go to the store and buy an emerald cut at that time.
I also think that a larger emerald cut will not suit your hands as well as what you have now. The rectangular shape's straight lines would not look as nice on your specific hands as the circle does. I feel that the sharp, dramatic lines of the emerald cut are best worn on hands that also have some angularity to them. Otherwise, the stone can overwhelm the hands and you have a case of "the jewelry wearing you rather than you wearing the jewelry." Also, I worry that a stone that is any larger than what you have, will be too large for your hands. An emerald cut would perhaps come too far up your knuckle and start to overwhelm your hand.
I honestly think the ring you have now is absolutely perfect for you. Both the size and shape are perfect for your hands. If you must change or add something, I would get a bigger eternity band.
Best of luck with whatever you choose! Great "problem" to have for sure!! Please let us know what you choose to do!