Counter job offer

Dear All, Need your advise please. I am working for a reputable large company in UAE for about 3-4 years with no salary increase. I know it is normal here, but still. Recently I received an external job offer with a better salary, my company gives me the counter offer by matching my external job offer. Now, I am thinking what to do… I read a lot about it, and it seems that there is a common belief that the company most probably will look for your replacement within 3-6 months after offering you the counter offer. What is your experience for such situations? And what is the common trend for employers/companies in such situations? Is it normal in UAE that companies will seek for your replacement while offering the counter offer? Thank you!

Some updates: 1. The new company is much less in size and by the revenue. 2. It is less recognized globally and within Middle East, which maybe later will not be so good for my CV. 3. To make the new job offer better, I negotiated it several times with a new employer.