Although African wild dogs (Lycaon pictus) and spotted hyaena (Crocutta crocutta) share similar habitats in Africa’s wild and protected areas, they are very different animals indeed.
Wild dogs very seldom steal kills from other animals, whilst spotted hyaena do so often.  Both animals are social, though wild dogs are almost always social, and hyaenas a bit more likely likely to move around alone at times.
Spotted hyaena are about twice as big as a wild dog, and have more powerful jaws.  Both these carnivores are able to kill prey animals larger than themselves and do so quite often.
I have been fortunate to witness interaction between the two species in the wild, and it can provide exciting viewing and photographic opportunities.

Driving out of Savuti Bush camp, we were following the Linyanti wild dog pack, when we lost sight and track of them.
This wasn’t unusual, as it can be very tough to keep up with wild dogs when they are hunting, especially when there are many large trees around.
Luckily, we relocated the dogs, and they were finishing off an impala alongside the water.  Most of the meat was gone, but one injured dog with a bad limp, was still eating.  The rest of the pack were lying down some metres away, in the woodland.  A single spotted hyaena approached quietly and quickly, and it rushed at the injured dog and its meal.

Spotted hyaena and African wild dog.
Canon 40D, Canon 300 f2.8 IS, handheld. Shutter speed 1/1000sec at f/8.0, iso 320.
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The next moment, four of the adult wild dogs exploded into action and charged at the spotted hyaena.  Despite it’s larger size, and more powerful, potentially deadly bite, the hyaena had no option but to give way.  The wild dogs were so fierce in their attack that the hyaena was forced to back into the Savuti channel, to protect its rear end by immersion in the water.
Wild dogs will target the hind-quarters of spotted hyaena during fights, and can really inflict damage, especially on a single animal.
This hyaena kept on moving into deeper water, until the dogs gave up, and it only came back after a long wait, once the dogs had moved off.
On other occasions, I have seen three or four spotted hyaenas drive a dog pack off its kill, but in this particular part of Botswana, that only happens when the hyaenas are in numbers.  A single spotted hyaena is attacked without hesitation by the wild dogs.  This can be different in other locations and at other times.  It can also depend on which of the animals is most motivated by hunger or need.

Spotted hyaena sometimes follow wild dogs, and even sleep nearby during the day, in order to get an opportunity to scavenge from the dogs when they hunt.  If the wild dogs do not have small puppies to guard, they do not usually expend too much energy on chasing such hyaena away until they are actually hunting or have a kill.

A wild dog investigates a skulking hyaena. Canon 30D, Canon 300 f/4 IS lens, handheld. Shutter speed 1/640s at f/10.0, Iso 250.

In the instance pictured above, a wild dog cautiously investigates a spotted hyaena that had been resting close to the sleeping pack of dogs all day long, and had now backed into an old aardvark burrow to protect itself as the dogs were just beginning to wake up and start moving off for their afternoon hunt.  No aggressive interaction took place during this sighting, and the dog just looked, sniffed and moved away, following the rest of the pack.  Once the dogs had moved off, the hyaena came out of the hole, and proceeded to investigate the area where the dogs had been resting.  The hyaena was looking for any food items that might have been left behind by the wild dogs.  Neither species will usually seek confrontation especially if there is no food or young animals to defend.  Occasionally spotted hyaena, especially younger ones, may eat wild dog droppings, which is not a pleasant thing to think about if you are not a hyaena.

Photographing wild dogs is challenging.  They typically move fast, and capturing action shots really requires constant concentration, as the interactions between the dogs themselves, and other animals like the spotted hyaena in the images above, takes place really quickly.  In fact, if you are not watching through your viewfinder or actually taking the images, it is very easy to not even realize what you might have missed.
I usually try very hard to focus on what the dogs are doing, as that can sometimes help with predicting an event.  I also shoot quite a lot during any sort of active sighting, and then sift through my images for those that I may wish to keep.  The dogs normally move too quickly and too unpredictably to allow a photographer too many chances to sit back and wait for them to move into good photographic poses or locations.

I also typically shoot fast shutter speeds, and having a zoom lens that can allow quick responses to subjects that change distances and angles rapidly can be most useful too.

I also try to get my own shooting position as close to the eye level of the wild dogs as possible.  Wild dogs are not that big, and if you shoot from there eye level, the images tend to have more impact, whereas shooting from much higher tends to make them look much smaller than they are.