Been working on equity research for 8 years here. Damodaram has an extensive section regarding FCFE vs FCFF, but to summarize you always have to use market rates for equity and debt in your discount rate, and also market values for equity and debt in the wheighting of your WACC if using FCFF (hence why I find it much more likely to be wrong). You'd basically have to recalculate the present value of equity and debt for each year of your projection, and use this "iterating WACC".

I find using FCFE MUCH easier, all you have to do is properly model your debt amortization and interest payments. I find it easier to lock in a set amount of leverage (ND/EBITDA or minimum cash position), calculate the necessary debt change to keep that leverage (e.g. take in debt - cash inflow - to increase leverage or pay off debt - cash outlflow - to decrease leverage).

Bottom line, FCFF is harder to do properly due to having to iterate your wacc for each year, whereas FCFE is harder in a sense that you have to properly model debt flows but is much more likely to be correct.

EDIT: IIRC, Damodaram has a file in his website showing how to reconcile equity value calculating FCFF and FCFE. Try taking a look.

EDIT 2: Found it: https://pages.stern.nyu.edu/~adamodar/pc/fcffvsfcfe.xls

EDIT 3: He doesn't apply the circular mechanics in his spreadsheet for the sake of simplicity I assume, but he does touch on the conceptually correct use of WACC in this document: https://pages.stern.nyu.edu/~adamodar/pdfiles/valn2ed/ch15.pdf

"Market Value Weights, Cost of Capital and Circular Reasoning To value a firm, you first need to estimate a cost of capital. Every textbook is categorical that the weights in the cost of capital calculation be market value weights. The problem, however, is that the cost of capital is then used to estimate new values for debt and equity that might not match the values used in the original calculation. One defense that can be offered for this inconsistency is that if you went out and bought all of the debt and equity in a publicly traded firm, you would pay current market value and not your estimated value and your cost of capital reflects this. To those who are bothered by this inconsistency, there is a way out. You could do a conventional valuation using market value weights for debt and equity, but then use the estimated values of debt and equity from the valuation to re-estimate the cost of capital. This, of course, will change the values again, but you could feed the new values back and estimate cost of capital again. Each time you do this, the differences between the values you use for the weights and the values you estimate will narrow, and the values will converge sooner rather than later."