Electronic viewfinder Pros:

• Potentially smaller and lighter camera bodies and lenses (particularly wide angle lenses)
• Can zoom in to verify precise focus and depth of field
• Can see (almost) exactly what the camera sees, even in low light
• Can superimpose more complex data over the image (e.g. zebra stripes, focus peaking); see note below.
• No mirror assembly to fail
• Quieter shooting (no mirror motion)

Electronic viewfinder cons:

• Uses significantly more battery power
• Lower resolution when not zoomed in (harder to judge focus by eye)
• Temporarily obliterates night vision when used in the dark, making it hard to get around
• Slight latency (worse on older gear)
• Unless combined with electronic front curtain, significantly longer shutter lag (because it starts out open)
• For cameras without a fully enclosed viewfinder, light from screen can annoy others
• For cameras without dual-pixel autofocus or dedicated focus pixels, significantly less reliable focusing

Note that it is possible to overlay some data over optical viewfinders, of course, such as focus point dots, boundaries of focus zones, and so on. However, transmissive LCDs are much more limited in terms of what can be superimposed practically, because they can basically only darken, not lighten the image.

Eventually, when transparent OLEDs make their way into DSLRs, this difference will go away, but as far as I know, they have not appeared in any DSLRs yet.