Semi gloss is more durable than eggshell, but I don't think the durability is increased so much so that anyone will notice a difference. Eggshell is usually fine for bathrooms, but as always sheen is generally a personal preference type of thing.

pearl is a nice finish, as I have it in the kitchen.

In MY opinion...

I'd use Satin.
If a youth or "teen" bathroom, Semi-gloss...although Satin could be OK.

Depending on your ratios, you'll probably have a Satin anyway!

Faron

In a high-quality paint, sheen is much less important than it used to be. Eggshell or higher is fine as long as there is mildew protection in the film (most products will say this right on the can). If you are going economy, then satin or higher is the way to go.

PG1 has a good point too...

The better the paint, the lower the sheen you can get away with.

My usual "from a technical-only standpoint ONLY" statement is still true though....

>>> Within any paint series, the shinier the film is...the "Literally" tighter/smoother the resin-film is. Therefore it's impermeability increases with sheen.

My own anecdotal info:
THANK G*D there's S/G in DD's bathroom!!
Looong hot showers/steam. Long ago, I drilled into her the importance of using the fan. Water-droplets still settle on the walls though. In that bathroom, there's still the better grade of a Contractors-grade S/G, applied 15 years ago. To this day, ABSOLUTELY NO problems with the walls/paint.
>>> Mainly due to the sheen-level of the lower-grade paint.

Faron