Is Trek Emonda ALR have thinner or thicker diameter tubing than the carbon model? I'm wondering if Trek Emonda ALR have thinner or thicker diameter tubing than the carbon model SL/SLR? I might actually get the aluminum one if it's thinner.
That's a question with multiple answers depending on what you're trying to find out.

From a distance the Aluminium and Carbon bikes look almost identical. 
 Compare these two Emonda bikes and see which you think is CF and which is Aluminium.  Try to ignore the wheel rims and different colour schemes, barsm stem, saddle, seatpost, and that both have a carbon fibre fork.




SE Bicycles doesn't offer the Spoiler markup tag.....
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The top bike is the aluminium Trek Emonda , and the bottom is the carbon fibre version of the same bike.

Differences:


The CF bike has visually chunkier tubing over the AL one.
The CF downtube appears to be consistent thickness whereas the AL one tapers thinner as it drops to the BB
That head tube on the CF bike looks enormous compared to the AL head tube.
CF bike has thicker chainstays and seat stays over the AL bike
The seatpost clamp area looks quite different too - the AL bike has tubes that stop at the welds whereas the CF bike has curves merging one tube around a corner into the next tube.


Curiously, the only tube that looks the same on both frames is the seatpost tube.

However the hidden difference is that the CF bike could be as much as a kilo lighter than the equivalent AL one.