A heavier draw does not necessarily equate to a higher power or a greater velocity.
Consider this - an average weight recurve bow may have a draw of about 40lbs and a crossbow 100-150lbs. This means that the crossbow is about three times more `powerful', right? Wrong.
It's wrong because, despite the increased draw weight, the crossbow actually stores much less energy, because its prod is much shorter than a bow, and the draw length consequently shorter. Energy is proportional to force multiplied by distance -- and the force required to draw a crossbow only reaches its peak at the last inch or so of draw.
It turns out that a 150lb crossbow at full draw is only storing about one third to one half the energy of a 40lb bow. For both military and hunting purposes, therefore, a bow is therefore much more effective, in terms of hitting the target hard, than a crossbow, when both are at the limits of what can reasonably be manufactured and used. The crossbow will typially shoot its projectile somewhat faster than a bow -- typically 200-220 feet per second, as compared to 180-200 feet per second. But that's because the crossbow bolt only weighs about a third as much as the arrow, not because the crossbow is more `powerful'.
This all means that a modern recurve bow of the type that is used in for target shooting is a much more fearsome weapon than the kind of crossbow you are likely to be able to buy from a mail-order supplier.