This was the first time that Logan had ever felt panic. Due to him having night vision in his helmet he was wearing, he was able to see the beast before it came into view. Peter could as well but was unaware of the magnitude of horror they were about the face.
Perhaps Peter didn't study as well at school and thought it was just a regular beast, or when he had evolved everything about him changed. Right now it didn't look like he could feel fear like the others.
Beasts were separated into different tiers. The tiers were based on the crystals that were embedded in their body. The more powerful the crystal, the higher the tier of the beast. This, however, didn't always mean they were stronger.
Depending on the beast's structure or abilities, sometimes in rare cases, there were those that were more difficult to deal with. This was unlikely the case because a higher tier beast would be able to draw more power from the crystal.