I don't think that these are valid assumptions. You're basically making a "trickle down" argument (if the rich do better, their heroic efforts will create so much economic growth that everyone benefits), and I would argue that our economic experience since 1980 argues pretty convincingly against that. In fact, studies on this topic (see http://www.fas.org/sgp/crs/misc/R42111.pdf) find virtually no correlation between top tax rates and overall economic growth, contrary to the belief of proponents of supply side macroeconomics.
I think the burden is really on you (or the supply side proponents) to demonstrate the truth of these long term economic growth claims, rather than just asserting them. In the absence of such proof, I would argue that concerns of economic equality and reduced suffering on the truly poor in our society far outweigh any of these nebulous assertions of promised future economic growth.
Finally, this doesn't have to be limited to a "welfare" vs. "investment" question. Government taking in money doesn't have to just give it out to people in welfare programs; it is perfectly capable of making investments too (infrastructure, basic scientific research, correcting market failures, etc.). There's no reason that a dollar invested by the government in infrastructure creates less growth than a dollar invested by a wealthy individual; in fact, given the propensity for wealthy individuals to park money in investments of questionable social value (see much of Wall Street's activities), I'd argue that the former is actually MORE beneficial to overall macroeconomic growth.