I have found a nether fortress where there are two blaze spawners that are pretty close to each other. However, they are not close enough for me to connect them, I think the gap between then is about 100 blocks.
I was wondering what the best way will be to deal with them. Should I just break one and focus one the other one, or is there a way to benefit from both of them.
I guess when I am busy with one them all blazes that have spawned from the other spawner will despawn.
It's probably not worth it to try to create some intricate, custom designed mob trap for both spawners. I would only focus on one, how many blaze rods could you possibly need? Unless, of course, you want to create an intricate, custom designed mob trap. I don't think anyone can help you on that, though, because I've never seen it done before (although I could be wrong). Whatever you choose, good luck!
Connecting spawners together doesn't make any sense unless (pythagorean) distance between them is less than 32 blocks, because you will not be able to have them both activated at the same time.
If you have one good trap, it can utilize a spawner at maximal efficiency; a second spawner far away wouldn't change anything. The important thing here is getting the mobs out of the so called "escape area" (17x17x9 centered on spawner). If there are 6 mobs in the escape area, the spawner won't produce any more mobs. More details about this are in this great video.
Working with Blazes is very hard unless you have a way of getting water into the Nether. The best Blaze trap that I've seen requires, for example, 32 sticky pistons and tons of other resources. There is an alternative design that is not maximally efficient or very easy to use. But it sure is easy to build:
One reason I can think of to connect both would be if you locate a base directly between and your normal movements inside would bring you into range of one or the other frequently. In this case, moving the blazes to a central location may be a convenience. Given the distance you mentioned (~100 blocks) I think you would likely not fall into this criteria.
This episode of Etho's Lab shows him building a vertical conveyor specifically for blazes.
If you plan to AFK though then just pick one or the other.
