Wouldn't worry overmuch if shots are less than 150.
I've shot my only fallow with a Federal Powershok 130gr out of a .270win. Roughly 200yds, H&L shot, couple steps and fell over. Subsequent examination showed that the bullet went through both atria and shredded the aorta. Damage wasn't bad at all really, decent expansion, nothing drastic and clipped the shoulder bone coming out the far side. I ate him with my uni house mates over the course of a couple months, and he was very tasty.
Moral of the story, if there is one, is that they aren't overly tough animals and within a couple hundred yards a basic cup and core bullet works just fine at a moderate velocity.
Of the two rounds you listed, I'd lean towards a 140gr fusion as a perfectly adequate bullet, so long as it groups. SSTs would work admirably, but might waste a bit more meat (he says with authority, based on no practical experience and exclusively on it having a polymer tip)