Weight Weenies

OP, if appearance is the main concern, I'd go for the clip ons and adjust expectations. Touring riders usually have clip ons with standard road bikes, and it's a look you do get used to. Check out some of the Indian Pacific Wheel Race competitors' bikes for good looking examples.

Otherwise, flat tops will be more comfortable if there is some padding, but I'd steer clear of any that are too cheap.

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i ride on the top of the bars and on the hoods as well. when i had round tubed handlebars...the round shape would dig into my forearms and could only stay in that position for a short time. i went to a set of aero Zipp bars to finally, the Enve SES road bars which i find very comfortable. and i have these bars on a non-aero bike (AX Lightness and Parlee SLi at the time).

I had aero bars (EC70's) on my Evo hi-mod which you can see on the first page of my build thread, but as others have mentioned, the sweaty slippery forearm issue is real with no tape (can be an issue with the wrong tape too, read Lizard skin DSP 2.5mm). I eventually switched back to 3T Ergonova's and added Supacaz Silicon tape to the tops and now the IAB position is much better and easier to maintain. Plus the slightly ovalized tops on the 3T bars are very comfortable unlike fully round tops.

I'd say if you use the IAB position, your aero gains from body positioning are much higher than what you give up from taping the tops or not using the most aero flat top bars.

If you have the aero bars for the aerodynamic properties wrapping it fully with bar tape doesn't make any sense....
If you have it because of its aesthetics or because of its comfort then ok.

yeah, flat-top aero handlebar is really helpful in TT position.
now i using zipp sl70 aero handlebar. TT position in this handlebar has more stable than tradition round handlebar.