Are they certain situations I would get one item over the other? Also, what are the pros/cons of picking either.
Other than stats, there is one important thing to consider about the respective jungling items: their passives.
Spirit of the Elder Lizard provides additional damage on basic attacks and non-DoT (damage over time) spells. This is extremely helpful for junglers with fast attacks speeds, like Udyr, or those with spammable abilities, like Evelynn. Each time you hit an enemy with your Q, you will deal small amounts of true damage. With the additional 10% cooldown reduction granted by the item, you can do a lot of sustained damage.
On the other hand, Spirit of the Spectral Wraith provides for slightly more durability with 20% spell vamp and added revenue with the decreased cooldown on Smite. This is very useful in the case that you are unable to run a good ganking game, either through enemy team comp or skill.
All in all, which item you pick is up to your playstyle. If you're a good ganker and find yourself getting a kill early, pick up Elder Lizard by all means. It will make your ganking power all the more stronger. If you instead find yourself unable to gank, you can make up for that lack of gold with the Spectral Wraith.