Epoxy Grout over Cement Grout?
For starters, you generally don't want to put new grout over old grout.  I won't say it can't be done, but your results may be inconsistent.  Though it takes more time and effort, it's worth it to get rid of the old grout, or at least most of it.  Grouting over old grout means your new grout will be pretty thin, and the old stuff might show through.  Definitely get rid of any loose existing grout, if nothing else.

As far as epoxy grouts go, they aren't for the faint of heart.  They have a shorter working time (they set up faster) and are much less forgiving than conventional grouts.  They're also not easy to remove, should you end up with excess grout somewhere.  Personally, I'd say if you have to ask, epoxy grout is probably not for you.  Obviously, I don't know your skill level, but that's my opinion.  As a non-professional, I personally will stay with the standard cement-type grout.

A few other pointers that people don't always think of:


If your tile has a glossy finish, I wouldn't use sanded grout.  The sand can scratch up and dull the tiles.  If you have the standard 4.25" square wall tiles, they usually self-space to 1/8" which is doable with either sanded or non-sanded grout.
Remove and replace the grout, and then go back and seal it (usually after 48 hours of drying).  Don't use the shower until it's been sealed.
Use caulk instead of grout between the bottom row of tile and the shower pan or tub.  Grout doesn't last long there.  Besides, you need to keep water out, and grout is porous (that's what the sealant is for).
(Very important) You have to reseal grout regularly.  How often depends on the sealant (some will last years, others need redoing every 12 months or so).  A lot of homeowners don't know that, so I bring it up whenever people are asking about tiling and grouting.


Tile work of any kind rewards thorough and meticulous preparation and execution.  You can't slap together a tile job and expect it to turn out looking great.  This isn't an accusation, just a boilerplate disclaimer.