Ok, given that I have no idea what LW does to MEC trooper stats, I'll give my 2 cents on MECs in vanilla EW. (note: I personally like using MECs, if only to cheese the finale and make it a cakewalk.)
1. MEC troopers gain less experience for a kill compared to a regular soldier (half the XP gain, iirc). Their Aim and Will stat increases also tend to be lower than a regular soldier. On a regular mission, this means that using a MEC as a regular soldier makes them rank up way, way slower than the rest of the squad. I suppose this feature is required to balance out the massive tankiness MECs offer.
2. MECs are a good option over SHIVs, for the following reasons: MEC troopers can rank up (unless they're already at Colonel rank); MECs typically have higher HP pools than a SHIV of similar tech level (eg. a basic SHIV has 10 HP, a level 1 MEC has a minimum of 8+5 HP); MECs have good killy AoE subsystem options compared to SHIVs; MECs are one of the only units to be able to lockdown Sectopods with minimal possibility of missing (the other unit is an Archangel 120 Aim sniper with disabling shot, a SCOPE and genemod).
On the other hand, SHIVs have the following advantages: they're expendable; can be improved through Foundry upgrades to suppress stuff, close combat reaction fire, infinite healing so long as the SHIV doesn't take a crit; lategame SHIVs can fly; SHIVs cannot be mindcontrolled; and finally, SHIVs don't need meld for production.