The real strength of the Teutons is in their castles. This can be useful but rarely makes a significant difference in the long run. Your monks have double the regular healing range. They can be useful in certain situations, but more often than not they tend to die needlessly.
However, they are also very slow, and even with all that armor they can be very vulnerable to ranged units and monks simply because it takes so long to reach your enemies not to mention that retreat is out of the question.
They are infantry units with an incredible amount of armor. The first thing most people notice about the Teutons are the Teutonic knights. They are extremely slow but almost invulnerable to most attacks. They have double the HP and attack of most other units, and cost almost twice as much too. Their unique unit is the Teutonic Knight, arguably the strongest infantry unit. Their towers and town centers have attack bonus, their monks heal your units faster, and their farms cost 33% less. Their major advantage is their economy, defensive technologies, and their extremely strong unique unit. With the Goths and Vikings, the Teutons are one of the civilizations belonging to the Eastern and Northern European culture.