Hi,
On the river we beat everything except Qsx and Asx, most notably Kx hands that might get suspicious you're bluffing and hands with a lower spade that might not valuebet when checked to but will certainly call a bet from us.
What that means is his calling range is wider than his betting range, hence leading out for value is better than check/calling. The only downside is that you have to be able to estimate roughly what he'll raise you with, as you don't want to bet/call if he's only raising Asx and you don't want to bet/fold if he's crazy enough to raise any flush. I'm bet/folding as a standard when in doubt.
Hope it helps.