I think I have a unique, or at least a less common, perspective on this from which to lend some advice. This is going to be long, the last paragraph is a shortened version. Stack Exchange is usually about solid answers with references and empirical data, but this is a subjective question on subjective matter.
I'll start with the 1 fact that applies to this question. There are many, many differences between the books and the show. These differences usually lie in the details, but there is such an immense amount of detail in the books that it all adds up to quite a bit of difference between the 2 mediums. I give an example of one of these differences below and talk about how small it is overall but how it still brings a lot to the book.
I did not read the books yet. I plan to start reading them very soon. The 3rd season of the show is about to end tomorrow evening.
In 3 seasons, much has happened. Very big surprises and twists and turns. My chief concern was that knowing these things before hand could make the books more boring than they would have been had I not watched the show.
I have since put that concern to rest after thinking about it bit more and here's why.
I knew some things about the story before they happened in the show. Some of the things I knew simply because the internet can be hazardous when it comes to popular media spoilers. Some of the other things I knew were from scouring the ASOIAF wiki. I would be reading about a character I like and read just a tiny bit too far and glimpse something huge.
I knew the details of the Red Wedding almost a year before it aired this season just last week without reading the books. I was still amazed at the scene in the show when it finally happened, just as I was with anything else I knew prior to it happening. Come to think of it, I might have known about every single major death before it happened and my enjoyment of the series wasn't as diminished as you might think.
Things are just so interesting in these stories that knowing some of the major plot points doesn't completely ruin the adventure. The journey to each of these plot points is just as good as the pay off and the small and sometimes very big differences in the books should be much more than enough to make it worth it.
It's akin to Romeo and Juliet. They tell you how it's going to end at the very start of it. You watch to find out how it happens though. This is a little different because I know what happens and how it happens. That means that the differences between the show and the books are the driving force behind continued reading of the books.
The main plot points will still happen and for the most part we will arrive at those happenings in much the same way as the show, but the different characters and added detail should be enough to keep it entertaining. George is a great writer from what I hear, the details the show doesn't have time for is what I'm betting on keeping me interested.
Slight spoiler ahead but not that big of a deal really. It has to do with the battle at Blackwater Bay. Tyrion's Chain, it was a pretty epic part in the battle before the wildfire was unleashed on Stannis's fleet. It's wasn't in the show. It was a gigantic chain hidden in the water. At just the right time the chain was pulled up out of the water and the ships crashed into it. I believe another chain was pulled up behind them as well to block any retreat. With the fleet now enclosed in the bay, the wildfire was then used on them. It's a minor difference against the big picture but it goes further in showing how smart Tyrion is. That extra description of the chains is enough to make that battle interesting to read on it's own even though I know exactly how it ends and why it started and how we got there to begin with, know what I mean?
So in short, I would say there is never a reason to not read the books besides the fact you're not enjoying them. Even if the show was on season 10, I feel the books would be worth it. I learned this the hard way, by being a spoiler hound but still enjoying the show. So I can only assume that I'll enjoy the books even with knowing everything, just as I did with the TV show. The books have the added benefit of extra details (TONS of extras) and minor plots to enhance enjoyment as well, no matter how much you already know from the show and wikis.
I finished the first book and am a little bit into the 2nd book. I have to say I PREFER having saw the show first! These books are not "easy" reads in my opinion and sometimes I find it hard to form a picture in my head based off of the book descriptions. Having seen the show though, I have A TON of visuals to pull from to enhance my understanding of scenes within the books. I think this coupled with all of the extra details and minor plots the show doesn't have makes reading the books a great companion to the TV show. Enjoying it very much.