I'd be careful about assuming that - a modern weapon is far more efficient than its historical counterpart.
A bit of digging indicates that most medieval crossbow prods only pull 4-6", while a modern one pulls 7-8" due to better quality steel and manufacturing tolerances.
Those couple of extra inches would allow for a significant increase in power, so assuming a linear increase in power out:draw distance, your 175lb crossbow could well equal a 350lb medieval one and hence match up against a decent draw weight Mongolian recurve.
This isn't allowing for any other design improvements that modern technology enables (release mechanism, modern string materials, etc).
Speaking of which, I wonder if a modern aluminium or a carbon fibre arrow would get the same sort of penetration as a traditional wood one? I'm thinking not since they're considerably lighter, but I don't have the equipment to test this out.
I'm also somewhat limited in the arrow heads I can obtain in this country due to laws on bow hunting (we're not allowed to so importing modern arrow heads might be a bit tricky).
I've several depictions of American Civil War officers leading their men into combat with pistol and saber - is this not accurate, or were automatic revolvers not fully reliable/effective yet?