Budget? These two lens may be similar in the focal length range but there are big differences too.
2) 18-135 is variable aperture, 24-105 is fixed f4
3) Build quality and image quality (24-105 is better)
5) 18-135 covers wider and longer focal length as it is designed primary for cropped camera like yours. 24-105 is designed more for full frame camera. If used on 600D then the widest equivalent field of vision on 24-105 is actually 24 x 1.6 compared to 18-135 which is 18 x 1.6.
Depending on your budget and purpose, it is not easy to tell you which we recommend unless you provide more details. Usually for new users I would probably tell them get a 2nd hand 18-135 and play with it first later then sell at not too big price loss when they want to upgrade. If buying 2nd hand 18-135 I would recommend used 18-200 instead.
If you are familiar with your camera already and have been shooting for some time, then 24-105 is a nice kit to invest in and use for long term.
The main thing here is not if the 24-105mm is superior in term of image quality as compared to 18-135mm. The main thing here is... what is the focal range you are talking about. If you need a lens that is as wide as 18mm (28.8mm on a APS-C sensor camera) and 135mm (216mm on an APS-C sensor camera) then you can only get the 18-135mm unless you fancy carrying more lenses to cover your entire range.
And in that aspect, no one here can help you. Because none of us know what is your criteria in term of focal range...
Why are you caught up? Have you rad some reviews? Have you seen the differences in size, quality and price? Are you able to recognize the differences in image quality? Or is it just the feeling of "Must have L Lens"?
Please ponder a bit more, share your thoughts and we might see where you are coming from. Right now I would repeat what has been answered many times: "if you need to ask then you don't need". So get the 18-135 kit lens, start walking and see where the road leads you to. There is a good reason why the 18-135 is sold as kit lens with the camera. Have a look at pictures taken with the 18-135 kit lens, learn to be on equal level.
A lens is not an investment, it's an electronic consumer product. The value drops the moment you leave the shop. If you don't know how to use it, its value drops even further.
(All of the above is pointless, of course, if you just want to spend the money. But then, why do you need to ask?)