Edited to say TLDR: I've given this a lot of thought!
The Bath house is lovely but living in that busy location in Batheaston and the Bath area as a whole wouldn't work for us as a family. We'd have a little holiday in it but would then have to sell it. I wouldn't keep it to rent out or holiday let as that would be too much risk and potential hassle for me. Having these as neighbours possibly visiting the garden would make it more tempting and certainly one of my DCs would be using a lot of pester power:
Otter sightings on the rise in the centre of Bath - BBC News
This Norfolk house though is more of a possibility for us. I wouldn't say no to winning either of them from a financial point of view, obviously, but if I had to pick one of the two to win it would definitely be the Norfolk one. I'd have to spend quite a chunk of the cash part of the prize on building a glasshouse over the pool so it could be used year-round, planting screening for privacy from the overlooking neighbours and putting up deer-fencing or similar to keep the dogs in, especially with the close proximity of the busy and fast coast road. One thing that puts me off is the traffic noise and pollution from the coast road in the peak holiday times.
We love Norfolk and have spent quite a bit of time there over the years in all seasons. We've visited Blakeney a couple of times and have walked to Blakeney Point in wild windy winter weather to see the seals. I'd recommend going on a boat trip to see them instead in better weather! We've stayed nearby in Cley (rhymes with spy) and Salthouse, up the coast in Brancaster Staithe and down the coast in Happisburgh (Haze-bruh) and Mundesley.
Some places and the roads do get busy at peak holiday times of course but Norfolk is the kind of place where you can usually get away from the crowds. I can understand some pps saying the location of the Norfolk house looks desolate from the photos. It can be of course when it's blowing a gale, grey or tipping down with rain, but it's a National Trust National Nature Reserve. Those creeks and marshes are teeming with birds and other wildlife. They are fantastic places for walking and dog walks. The nearby sandy beaches at Wells and Holkham are lovely and there are some good market towns in the area, like Holt. There are plenty of good independent shops around and the supermarkets deliver. It takes about an hour to get to the very nice city of Norwich.
I agree with pps that it almost certainly isn't worth Omaze's £6m valuation but I think we could live in that house very happily with a few tweaks. I'd like to win it anyway and try an extended stay to see if we could make it work. One DC, who is a young adult now, might take a bit of convincing, not on the house but on the location as it's about twice as far to a city than we are now. Fingers crossed here anyway! As it would be for most people, it would be completely lifechanging to win whether we lived in the house or not.