Alfvén ion cyclotron waves (ACWs) and kinetic Alfvén waves (KAWs) are found to exist at <0.3 au observed by Parker Solar Probe in Alfvénic slow solar winds. To examine the statistical properties of the background parameters for ACWs and KAWs and related wave disturbances, both wave events observed by Parker Solar Probe are selected and analyzed. The results show that there are obvious differences in the background and disturbance parameters between ACWs and KAWs. ACW events have a relatively higher occurrence rate but with a total duration slightly shorter than KAW events. The median background magnetic field magnitude and the related background solar wind speed of KAW events are larger than those of ACWs. The distributions of the relative disturbances of the proton velocity, proton temperature, the proton number density, and β cover wider ranges for ACW events than for KAW events. The results may be important for the understanding of the nature and characteristics of Alfvénic slow solar wind fluctuations at ion scales near the Sun, and provide the information of the background field and plasma parameters and the wave disturbances of ACWs and KAWs for further relevant theoretical modeling or numerical simulations.