Winchester's a funny place. There are plenty of streets, within spitting distance of the city centre, where house prices can be 100k less than comparable houses in the next street along. It can all seem a bit random to newcomers and sometimes, if I'm honest, to residents. There are, however, usually reasons.
School catchment is one. Anything in catchment for St F's is ££££ - and often teeny-tiny. St B isn't that far behind, which probably also helps explain the discrepancy between house prices in Hyde and Fulflood.
As far as Brassey Rd goes, it's pleasant enough but the houses tend to be smaller than in nearby roads. The house you've identified also hasn't yet been extended, which may also have affected its price.
FWIW, Hatherley Rd has some of Fulflood's most expensive houses (some of them now £1m +). Fairfield Rd is probably no. 2 in the price comparison chart of the network of streets surrounding Peter Symonds. (I'm excluding Cheriton Rd, which is even pricier and I'm not quite sure if it's actually Fulflood.) In Hyde, Arthur Rd tends to be the most expensive (again, the biggest semis there are now going for north of £1m). In the city centre, it's Parchment St.
I'd be wary of Water Lane. Some of the houses there flooded in 2013 and although Winch now has excellent flood defences, I'd want to be sure I could get mainstream insurance easily. (This may be OK as I have an idea that the government has implemented measures to ensure that everyone can access insurance, even in flood risk areas.)
Another factor to consider is traffic and parking. The city centre is gridlocked much of the time and you'd have no way of avoiding that in Hyde. Bit easier in Fulflood. Also parking spaces are often very hard to find and, as you'll have seen, few houses have garages or off street parking.
I used to live in Hyde and loved it but moved out (to one of the villages) for more space. As a PP said, it is VERY sociable and friendly but also, frankly, a bit goldfish bowl-like, if you know what I mean.
Sorry, essay. Hope you find somewhere you love.