Interchangeable Lenses
The number one reason for choosing a SLR camera (film or digital) is that SLRs are camera bodies onto which you can mount a whole library of lenses. [Note that most DSLR cameras use an APS-C sized sensor, resulting in a focal length magnification of 1.5x. So that a 300mm lens results in a focal length of 450 mm. The Olympus, which uses a smaller - hence noisier, all else equal - sensor has a magnification of 2.0x.]

High Speed
Baseball is often played at night and it requires a camera that can freeze action with a fast shutter speed. To do either or both requires an image capturing device that is very responsive to light. Film cameras can change that response by changing film - ISO 100 (older designation was ASA instead of ISO) is least responsive. Want to use lower light? Change to ISO 400 film. You can't change the CCD or CMOS sensor in a digital SLR, though. But all digital cameras can change ISO sensitivity on the fly with a dial or menu change. DSLRs all offer at least ISO 1600 (some 3200), but EVF (electronic view finder) cameras often top out at ISO 200 or 400.

Creative Control
SLRs give you maximum control over ISO, shutter speed and lens aperture (size of lens opening) settings so that you can exercise control over motion blur and depth of field.

Cost
EVF (electronic view finder) cameras are cheaper than DSLRs. The body of a DSLR may not be much more, but then you start adding lenses. Some lenses cost $100 while others cost $10,000. You can expect, though, that you'll spend at least $300 on top of the cost of the "kit" lens that comes with a DSLR. That's just getting started. Obviously you can spend much more. And to get a good low-light lens for night games you will pay more.

You Don't Have to Change Lenses
The other side to the SLR interchangeable lens story is that you have to change lenses with an SLR camera. The whole idea of a superzoom is that you have a wide latitude in changing zoom magnification with the same camera. And that's handy! [Of course you can get a long zoom DSLR lens that matches the magnification ratio of these superzooms. But those typically are not "fast" lenses (good for low light).]

Dust
More precisely, the lack of dust. Every time you change the lens on a DSLR camera you allow the possibility that dust will enter the camera and attach itself to the image sensor. This will create specs on the images. Professional cleaning is expensive. So if you choose a DSLR be careful about dust and consider a camera - from Olympus, Sony, Canon or Pentax - that has a dust prevention and/or removal system. [The Olympus system is the best here.]

Video
EVF (electronic view finder) cameras, including superzooms, essentially are showing you a TV picture of the image you're recording. SLRs, on the other hand, allow you to see exactly the optical image coming through the lens to the image sensor. The former approach means that EVF cameras can also be used to record video sequences, much like a videocamera. You wouldn't want to shoot a whole game on video using an EVF digicam, but it's great for short segments such as a pitcher's delivery or sliding into 2nd base. You just can do that on a SLR.

Live Preview
You can compose a picture on the LCD screen of a EVF superzoom camera, but you cannot on a DSLR (except for the Olympus and Panasonic cameras which have a separate sensor for this). The LCD screen on a DSLR is just for viewing menu options and pictures already taken.