What are the main differences between a strategy's Sharpe ratio, and its alpha based on the Fame French factors? Does it make sense to evaluate them both in a thesis?
A Sharpe ratio gives you a return per unit of risk as @KeSchn wrote. For investors, A Sharpe ratio is generally a good comparison measure between different portfolios. You can only compare Alphas if the benchmarks are the same.
The best comparison is one you can make with portfolios with equal variances (e.g. scale variance to 10 or 20% depending on your sample for all your portfolios) and then compare Alphas if they have the same benchmark.
I would show mean excess return (over the risk-free rate), mean risk-adjusted return (Alpha), Sharpe Ratio (Mean excess-return/standard deviation) and market beta (beta with your benchmark).
Make sure to annualize these. For the Sharpe Ratio monthly to Yearly you can multiply with square root of 12.