From chatting to some of the Quins staff about it, the main monetary value to the club is in the home fixtures. Having a tough or at least interesting draw in the Champions Cup pretty much guarantees sell out home matches, as does a home QF, and that's of huge value to the club. I don't think prize money really enters into it unless you have a serious chance of winning the thing - and even then I suspect the impact of having a recent trophy on season ticket sales and home attendance outweighs the value of the prize itself.
A good starting point for understanding clubs' economic priorities is that home games are the big determinant of profit and loss. Things like TV and sponsorship revenue are fairly fixed in any given year, and spend at the ground is the main thing the club can influence during the course of the season. Anything that helps to fill the seats is great, and it also explains the weird design of things like the Anglo Welsh and Premiership cups - things like playing a different pool rather than within a group are designed to ensure that everyone gets enough home games without using up too many match dates.
The year we had a really easy champions cup group, the club went all out to get a home quarter as it was the only way to get enough revenue out of the competition. And we ended up hosting Munster, who tonked us, but it was a tonking in a stadium full of Irishmen who spent handsomely on booze.