I actually haven't taken a bath as an adult.
Well. Without googling it I can tell you what my thoughst are... (talking about a hot bath)
Instead of a shower your whole body is in the water which relaxes your entire muscular system I guess.
And can have a very mellowing effect on your mental state.
I take a bath at my dad's (don't have one myself) perhaps once a month with a large portion of epsom (magnesium) salt for an average of 90 minutes.
It relaxes all my muscles.
A shower is more for cleaning (although a long hot shower does have it's relaxing effects, I know) It's been around or nearly 2 years of daily cold showers which also have lots of benefits.
These are just my experiences just so you know. You're missing out friend. On both =P