Rogue:
Excellent mellee dps - Will do VERY high consistent dps that is sustainable until you die.
You will find it very hard to solo, and hard to duo. Because of your never ending high dps, groups will be eager to recruit you. That being said, your pretty SoL without a group. Pretty worthless as a tank, and your dps will be bad if you are facing the mob. Once you get a fair number of aa's, you can get the ability "escape" which will allow you to instant drop all agro from any mob. This will allow you to die somewhat less frequently than most classes.
Monk:
Good mellee dps - Will do considerable consistent dps that is sustainable until you die.
You will find it difficult to solo, but decent at duoing. Groups will enjoy having you because of your ability to split tough pulls, good sustainable dps, and the ability to tank/take hits if your gear is decent. It will be in your best interest to group or duo. Furthermore, you can tank/offtank well at the high end. Also because of your ability to feign death, you can escape many deaths.
Difference:
Rogue is the mega mellee dps for raid/groups. Can't beat it. Monk is far more versatile (can take hits/tank), and split, but a bit less dps.
Essentially your trading your ability to take hits and split for more dps by going with a rogue over a monk.
Demand:
Groups/Raids: Rogues/Monks are in equal demand.
When I played, there were more monks then rogues. Thus, the rogues that do play are generally more sought after. However, I would recommend playing whichever you enjoy most.
Another note on raids: You can raid fine without a rogue. But if your raid lacks a puller, it can seriously slow down the raid and/or put it at a higher risk of wiping. Thus, monks are nearly mandatory, whereas a rogue can be replaced by any other dps class (generally at a slight loss of dps).
In your time lfg:
You will be jerking around for the most part on both classes. More so as a rogue than a monk (who has the ability to duo) and will solo far better than a rogue. When farming, a monk will be far superior to a rogue. There are also a few niches where a monk can solo to make decent xp/money.