Congratulations on convincing your husband to give it a try. It is a very special evening to me.
We have done both. We've dined at the Chef's Table once for our 23rd anniversary and probably 4-5 (maybe 6) times in the dining room. The Chef's Table affords you a view of the preparation of the meals and interaction with the chefs. You sample more dishes than you might in the main dining room...I think. It is more interactive.
The dining room is much more romantic for me. I'm very glad we had our Chef's dinner. But for us it will probably remain a singular memory.
Hopefully some more V&A fans will weigh in. Uncleromulus is our resident V&A expert and perhaps he can help you.
BTW, my husband and sons wear their jackets on the plane...easiest way to get them there in our experience.