Yes, that may be due to graphics. Does one have more graphics power than the other? If so, make sure that, in the CIV4ArtDefinesUnit.xml file, your code points to the same file in both <NIF> and <SHADERNIF> lines.
For example, my japanese infantry code is like:
<UnitArtInfo>
<Type>ART_DEF_UNIT_INFANTRY_JAPAN</Type>
<Button>,Art/Interface/Buttons/Units/Infantry.dds,Art/Interface/Buttons/Unit_Resource_Atlas.dds,8,3</Button>
<fScale>0.44</fScale>
<fInterfaceScale>1.0</fInterfaceScale>
<bActAsLand>0</bActAsLand>
<bActAsAir>0</bActAsAir>
<NIF>Art/Units/Infantry_Japan/Infantry_Japan.nif</NIF>
<KFM>Art/Units/Infantry/Infantry.kfm</KFM>
<SHADERNIF>Art/Units/Infantry_Japan/Infantry_Japan.nif</SHADERNIF>
<ShadowDef>
<ShadowNIF>Art/Units/01_UnitShadows/UnitShadow.nif</ShadowNIF>
<ShadowAttachNode>BIP Pelvis</ShadowAttachNode>
<fShadowScale>0.9</fShadowScale>
</ShadowDef>
<fBattleDistance>0.35</fBattleDistance>
<fRangedDeathTime>0.05</fRangedDeathTime>
<bActAsRanged>1</bActAsRanged>
<TrainSound>AS2D_UNIT_BUILD_UNIT</TrainSound>
<AudioRunSounds>
<AudioRunTypeLoop/>
<AudioRunTypeEnd/>
</AudioRunSounds>
</UnitArtInfo>
In my older computer, I have a unique-style japanese infantry. But in my other computer, the japanese infantry have the original graphic. I have the same problem with all my unique style units.