It's a really good question, very hard to answer. We're all desperate to make a splash nationally, I know that. Not only has Iowa basketball hit some really low points over the past couple decades, but this team in particular has been very endearing I think. They've been a lot of fun to watch them mature and develop.
My inclination is, if I had to go with one or the other, I'd go for the deep tourney run. Nationally, I'm not sure anyone really takes note of who wins their conference, but everyone takes note of who is in the final four. Likewise, no one looks at the final four teams and talks down on one of the teams for not having won their conference.
That said...with it being such a long drought since the Hawks won the Big Ten...man, it would be nice to have that monkey off our back. But that is more like a treat for the fan base. In the wider picture, it's all about the tourney.