I would suggest this specification that can comply with that budget.
Processor - Core i7 4th or 5th (6th is too costly)
RAM - 8GB
Graphics Card : A GT from the NVidia 800/900 series . (GTX can be costlier especially the latest series so, I would suggest for that budget a GT) its can be a 920M or a 940M etc But go for the latest architecture.(Maxwell as Pascal is too costly for a lappy)
HDD - 1TB OR 2TB OR 1TB with an SSD allotment
OS Windows 10( not other way as it comes default while buying a lappy) )
I think with these specs you can do a pretty decent gaming
those charateristics of the first one are almost the same, only video card is better (i have 840m gb), stil this laptop is 600eur more expensive than mine ? :O plus i have 17,3" screen..... so where s the points of 600 euros?! is graphic card 600 eur more expensive or what i dont get that... plus i have ssd disc which the first one doesnt have it, ok, maybe is processor little stornger, dont have such mhz power than this one...stil dont get it why such difference... aint that too much 1500 for laptop anyway?
Unless it's important that the PC is portable, I would recommend to buy a PC or hardware parts for probably less money and more power.
Gaming laptops are quite expensive, you would get a normal laptop for 500-600 € if you want a new one. I don't play on notebook, but I can imagine that it's worse than playing on a Desktop, I can't believe that games run smoothly on them, just because common laptops are not really built for gaming.
If you need a laptop due to studying, you should go for an Intel i7 processor at best, or at least a proper i5 of the 7th generation, it should have a good GPU that it can run games like MW3. I didn't hear anything bad about Lenovo yet. I just googled for "ultrabooks" and found some Lenovo models with i5's in the budget of up to 600 €. I don't really know about Notebook GPU's.
But you definetely should do good researches for specific hardware parts like for CPU and GPU, for example watch benchmarks, compare hardware / read reviews / find videos or anything which proves how a game works with a specific GPU and CPU for example .. etc.
You should ask some people who are using Notebooks for playing, I think they have more experience with gaming on laptop. I didn't play much on laptops yet, at least not cod's etc.
study->laptop should be more usefull gaming->PC desktop
idk. but a sheep laptop and gaming PC. Maybe the differences on price if u get 1 or both, when in balance with performance of both needs (gaming+study). But if u have to decide to buy one what rules is balence between money& needs
If you really need a laptop buy a chrome book or something on those lines(depending on how you use it)With the given budget,a good laptop is difficult.Buy a cheap laptop for work and build a good gaming rig(you will probably save a lot of cash that way) NOTE:this is being said by a gaming laptop user ._.