A wireless microphone relies on a receiver and looks nice. They can be place on a microphone stand next to the officicant and one can be placed close to the couple so you can hear their vowels. A concern for wireless microphones is it may drop the signal. Wireless microphones can work well but there is always a slight chance of the signal dropping or the battery running out of juice. It can be tested before the ceremony and work well but with wireless technology it can drop at any moment. 

A lapel microphone is placed near the collar. One does not need to hold it with the hands so the hands can be holding a book or other objects. The speaker can talk normally and the sound is sent to the speaker. Since the lapel is wireless there is a slight chance that that the signal may drop. Also if the lapel is turned on early, guest may hear the groom say something before the wedding starts that can be embarrassing. With the wind, it can be heard on the speaker since the lapel is sensitive and there is a slight chance of feedback. 

A corded microphone may not look as fancy as a wireless microphone or a lapel but one does not have to worry about it dropping any signal. It can be put on a microphone stand so it does not need to be held. 

It does not matter what microphone you chose there is always a chance of feedback. It happens when the speaker moves in front of the speaker or standing in certain areas. It is the dj’s job is lower the volume of the microphone and gradually increase the volume.