I believe your hypothetical is mathematically impossible, and the reason why is why the capital light company will outperform. Let's assume two companies, Company A earns 50% on equity, and Company B earns 20% on equity, both grow earnings at 20%, both earn $1 in year zero, and both have returns on incremental equity that are identical to their historical ROEs.
By hypothesis, Company A's starting equity will be $2 (1/2 = 50% ROE), and to earn $1.20 it would need to reinvest $0.40 of earnings from year zero (.40 * 50% = .20). It has an extra $0.60 in earnings from year zero that it can use to dividend out, buyback shares, etc.
By hypothesis, Company B's starting equity will be $5 (5 * 20% = 1). To earn and additional $0.20 it needs to reinvest all $1 of its year zero earnings (1 * 20% = .2) In other words, the more capital intensive Company B would have had to reinvest all of its earnings from year zero to obtain the same 20% growth.
So, if companies have different returns on equity, they can have the same earnings growth rate, but they will not have the same free cash flow left over after accounting for the earnings that had to be reinvested to achieve that growth. The difference between the amount of earnings the high ROE company had to invest versus the lower ROE company will be the source of the higher ROE ("capital lite") company's excess returns.