Two moody sounding chords which work well together or can be used on their
( they make nice ending chords in their respective keys )
The Emaj13 shape shown below can be played without the 4th finger on the fifth string as long as you avoid this string.
Having the 4th finger free means you could add extra melody notes to an arpeggio - experiment for yourself.
I have played two basic arpeggios on the soundfile which plays the tab twice.
Although these are good arpeggio chords they can also sound good strummed
( you would need to put the 4th finger on the Emaj13 for this )
If you want to play along this is a looped version of the soundfile