Since the votes are now mostly about of ships vs mecha, I have several arguments for the ships.
1. Cost of lives and materiel: In terms of pure materiel, ships have been said to need 'priceless Menschy matter' in order to be constructed, while nothing special or particularly limiting factor has been said as much for mecha. In terms of lives lost, the loss of mecha results in loss of individual lives per mecha lost, while losing ships results in the loss of of potentially hundreds or more lives per ship.
2. On supplies and salvage: When considering the result of the battle, losing mecha would result in the loss of the weapons and ammo on those mecha only. But when considering when ships are lost, basic supplies such as food, water and medicine would be lost, along with ammunition, spare parts, and everything else to keep both the remaining ships and mechas functional would be lost. As for why those supplies can't be simply salvaged from the destroyed ships, one must first think about how much of those supplies could even survive the destruction of the ships in the first place, given the type of suicidal last ditch attack that the fleet is suffering from. Then, one should also remember how time limited this mission is in the first place, and as such how proper salvaging was never a real options to begin with if this mission aims to succeed at all.
Thus when considering the end result, one has to compare either having most of the mechas survive, but having to deal with an under-supplied and overloaded fleet, and the loss of much less replaceable ships, vs having most of the ships survive, while having more than enough supplies for every surviving mecha and the entire rest of the fleet, and the loss of the much more easily replaceable mechas.