The three elements I have chosen to compare between MusicXML and MEI are: dynamics, clef and note.
Dynamics in MusicXML are represented by the dynamics element. This element is used for dynamic markings that are represented by text on the score. "Wedge indications" (crescendo, diminuendo) cannot be represented by the dynamics element. The children elements represent what type of dynamic is to be used; MusicXML uses abbreviations for the different dynamic markings, for example sf for sforzando. A constraint of this element is that it requires a placement attribute. The note element's placement attribute is used when the dynamics are associated with a particular note.On the other hand, the direction element's placement attribute is used when the dynamics are associated with a direction.
Dynamics in MEI are represented by the dynam element. Like MusicXML, this element is used only to represent dynamic markings which are represented by text. For example, forte (f), piano (p) or mezzo-forte (mf). This element cannot be used for dynamics represented in other forms, like a crescendo or diminuendo which are represented graphically. A constraint of this element in MEI is that it must have a specified starting point (if one is not stated, then this is considered a semantic error), using one of the following attributes: startid, tstamp, tstamp.ges or tstamp.real. Whereas an ending point can be specified, but is not required.
In MusicXML, clefs are represented by the clef element. A child element known as sign is required in order to specify the type of clef that is going to be used. The parent element of clef known as attributes is required. This element concerns musical elements like key signatures, time signatures and clefs. Clefs in MusicXML will automatically be added to the default position (the start of the stave), unless stated otherwise with an attribute. Using the additional attribute will allow you to add clef in a non-standard position, or add another clef on the same line of music. The additional attribute will be set to yes.
In MEI, the clef element is used specifically in the cases where you want to use a non-standard clef position, multiple clefs on a single stave, or you want the clef to have a specific size or colour. If using this attribute to change the clef size, the constraints are that the clef's position must be equal to or less than the number of lines on the stave. If a standard clef is required, then one would use the staff element's clef attribute. Unlike MusicXML where you use the clef element regardless.
In MusicXML, the tie element is used to indicate that a tie will start or end on this note. MusicXML uses the tie element to signify the sound of the tie only, and not the visual representation on the notation. In stead, for this, MusicXML uses another element:tied. To join two notes together, you would use a tied element with the attribute type="start" on the first note, and again the tied element with the attribute type="stop" on the last note. type="let-ring" is used with the tied element if the tie represents that the notes should be played undampened. The tied-type attribute is necessary when using the tied element, otherwise there will be no start or end point specified for the tie.
In MEI, there is only one tie element, as opposed to the distinction between tie and tied that MusicXML makes. Like MusicXML however, the tie element in MEI needs to have an established start point and end point with the startid and endid attributes.