I stopped playing the XCOM franchise after XCOM: EW was released several years ago. I recently wanted to start playing XCOM 2, but decided to finish a play-through of XCOM: EW first. Just as before, the sleeveless armor vest models for genetically modified soldiers was really annoying to me. Fortunately, it is really easy mod XCOM to use the standard armor models for these soldiers.
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Installation by File Replacement

If you'd like, you can use the mod file here to simply replace the appropriate file with my armor settings. This mod keeps the sleeveless model for Kevlar armor, but reverts to standard for all the other in-game armors (Carpace to Titan).

The file you want to replace is located here:

%USERPROFILE%\Documents\My Games\XCOM - Enemy Within\XComGame\Config\XComContent.ini
or, if you use OneDrive, here:

%USERPROFILE%\OneDrive\Documents\My Games\XCOM - Enemy Within\XComGame\Config\XComContent.ini
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Installation by Editing

You can also skip the file download and just edit the INI file yourself. Go to the XComContent.ini file referenced above and open it with a text editor. The lines you are looking for are these:

UnitPackageInfo=(PawnType=ePawnType_Female_1_Kevlar_GM,ArchetypeName="Soldier_FemaleKevlar_GM.ARC_FemaleKevlar_GM")
UnitPackageInfo=(PawnType=ePawnType_Female_2_Carapace_GM,ArchetypeName="Soldier_FemaleCarapace_GM.ARC_FemaleCarapace_GM")
UnitPackageInfo=(PawnType=ePawnType_Female_2_Skeleton_GM,ArchetypeName="Soldier_FemaleSkeleton_GM.ARC_FemaleSkeleton_GM")
UnitPackageInfo=(PawnType=ePawnType_Female_3_Archangel_GM,ArchetypeName="Soldier_FemaleArchangel_GM.ARC_FemaleArchangel_GM")
UnitPackageInfo=(PawnType=ePawnType_Female_3_Ghost_GM,ArchetypeName="Soldier_FemaleGhost_GM.ARC_FemaleGhost_GM")
UnitPackageInfo=(PawnType=ePawnType_Female_3_Titan_GM,ArchetypeName="Soldier_FemaleTitan_GM.ARC_FemaleTitan_GM")
UnitPackageInfo=(PawnType=ePawnType_FemalePsi_GM,ArchetypeName="Soldier_FemalePsi_GM.ARC_FemalePsi_GM")
UnitPackageInfo=(PawnType=ePawnType_Male_1_Kevlar_GM,ArchetypeName="Soldier_MaleKevlar_GM.ARC_MaleKevlar_GM")
UnitPackageInfo=(PawnType=ePawnType_Male_2_Carapace_GM,ArchetypeName="Soldier_MaleCarapace_GM.ARC_MaleCarapace_GM")
UnitPackageInfo=(PawnType=ePawnType_Male_2_Skeleton_GM,ArchetypeName="Soldier_MaleSkeleton_GM.ARC_MaleSkeleton_GM")
UnitPackageInfo=(PawnType=ePawnType_Male_3_Archangel_GM,ArchetypeName="Soldier_MaleArchangel_GM.ARC_MaleArchangel_GM")
UnitPackageInfo=(PawnType=ePawnType_Male_3_Ghost_GM,ArchetypeName="Soldier_MaleGhost_GM.ARC_MaleGhost_GM")
UnitPackageInfo=(PawnType=ePawnType_Male_3_Titan_GM,ArchetypeName="Soldier_MaleTitan_GM.ARC_MaleTitan_GM")
UnitPackageInfo=(PawnType=ePawnType_MalePsi_GM,ArchetypeName="Soldier_MalePsi_GM.ARC_MalePsi_GM")
NOTE: In the original file, these are not all in a nice block as you see here. These lines are sorted, and there are other values in-between these that I have removed from the example.

Delete the "_GM" parts from the key values. For example

UnitPackageInfo=(PawnType=ePawnType_Female_3_Titan_GM,ArchetypeName="Soldier_FemaleTitan_GM.ARC_FemaleTitan_GM")
becomes

UnitPackageInfo=(PawnType=ePawnType_Female_3_Titan_GM,ArchetypeName="Soldier_FemaleTitan.ARC_FemaleTitan")
Do that for all of the armors with "_GM" in them that you want to modify.

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Compatibility

The mod file is taken from an unmodded installation of the Steam version of XCOM: Enemy Unknown, so I know it is compatible with that. It is probably NOT compatible with any mod that changes the XComContent.ini (including Long War). However, manually editing the file should always work as long as doing so doesn't undo a change that another mod you are using makes.