The ilyama got freesync. If you have a amd graphics card this will be an awesome addition. It also got 75 hz! If you have a nvidia graphics card you can now try and experiment with gsync on freesync monitors but it might not work.
Either way I'd prefer the ilyama over the Asus.
Regarding TVs: there are Tests and tables nowadays to check the input lag etc. Normally TVs have a significant lag that you really don't want for gaming!
Some brands got gaming modes to reduce it like Samsung and Sony. I have no clue about the latest 120hz TVs etc but I know a 200 pound sharp TV will probably not have a gaming mode and therefore a huge input lag.
Maybe but though - you should research!
Monitors have a tiny input lag. Some have a bit more but nothing to spend thoughts on!
Additionally: TVs mostly have a clearer semi glossy surface coating. Resulting in a clearer image quality but if you got a lamp or the sun or whatever reflecting on it, you'll be a lot more bothered by this compared to the muddier coatings of standard monitors.
I personally searched for a clearer coating monitor specially. All lamps are behind my monitor of in angles I can't see their reflection and the clarity is awesome.
My TV on the other hand... Always have to shut off one of my lamps when entering a darker area in a game or watching some darker content.