Last year my wife and I rented a couple of SOT kayaks and used them to paddle around our local lake. We enjoyed it so much we have decided to purchase our own this year.
We are looking at some entry level kayaks to use at the lakes and rivers here in Illinois. 
I am also an avid fisherman and I would like to get a fishing kayak but I don't know if there is a difference, performance wise, between a fishing kayak and a touring/recreational kayak. I don't want to struggle to keep up with my wife if we decide to kayak for 4 to 5 hours on a river or lake.
Would I be able to use a fishing kayak like a regular touring/recreation kayak?

Thanks
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Yes, there is definitely a performance difference between different types of kayaks. In fact, there are performance differences among the same types of kayaks. For example, a 14-foot kayak will always track more straightly than a 10-foot kayak. A wide recreational kayak will always have more primary stability than a narrower touring kayak.

Even if you both get the same type of kayak I suspect you'll find they work differently for each of you. No doubt you both do not weigh the same -- if you're heavier, a given kayak will sit lower in the water than for her. That may result in increased stability, or it could mean that you capsize easily. Alternatively, consider height and armspan: if she's short she may find it difficult to paddle in a wide rec kayak where the paddle is constantly bumping the edge of the boat.

In short: you should each look for a kayak that suits you. That means you will see performance differences between the two kayaks, but if the boats really do suit each of you, that won't be a problem because you've found something that fits well. As to a fishing kayak specifically, if you get a longer kayak than her you'll likely be able to keep up with her on a day trip (though at the expense of maneuverability).

Of course, keeping up with a partner is about more than the just the kayak. The paddle will also make a difference (especially its weight as it relates to your fatigue), and paddling technique can be a big difference between feeling good at the end of an outing and feeling whipped.
I would recommend checking out something like Hobie's Mirage pedal driven kayaks. With their spiffy pedal drive, you can trivially outrun(outpedal?) just about anyone while hardly breaking a sweat. Additionally, because you power yourself with your feet, your hands are free for fishing. The mirage drive is also quiet as a corpse. No splashing sounds from your paddles, whatsoever.

A guy I know has one of their fishing-specific models, and loves it.

However, if you ever want to go on an overnight camping adventure via your kayaks, the storage capacity of the Hobies is pretty bad, and while in general portaging kayaks is no fun, portaging a Hobie kayak would be especially miserable.

Otherwise, you could try getting a tandem traditional kayak. Perhaps you can sweet-talk your wife into paddling while you fish?