I don't get eye-strain from reading on LCDs and the weight doesn't bother me either, I have no problems holding either of my two tablets (Original Galaxy Tab and a Transformer Infinity) in one hand, although I need to turn pages with my other hand using the ten inch tablet though.
I find no issues with the quality of the text on screen either. Using Mantano on a Transformer Infinity, to me has a much cleaner, crisper text than on my eInk readers. Although my new Aura HD may change my opinion on this.
In sunlight, yes the LCD readers may struggle a bit - especially my Galaxy Tab - but I still find they are usable. Ok I live in the U.K. and strong sunlight is not as commom here, but it can get pretty bright.
For me, I use whichever device is at hand, I couldn'd care less if it's a tablet or an eInk reader.
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