A answer has been accepted here - and it does make some valid points, but did not mention reflected amplification attacks; with tcp only small amounts of data are exchanged (and must be exchanged between both the attacker and victim) before processing, memory and io resources can be consumed. A slowloris type attack as described by Elias exploits a constrained number of connection resources. However there are a number of differences with udp.
Firstly the request from the client to do something can be in the first packet sent by the client.
A consequence of this is that the attacker can forge the 'from' address on the packet - making it difficult to detect an attck, nevermind block it.
There are some udp protocols where a single small request can generate a much larger response - such behaviour was present in the DNS and NTP protocols. This is exploited in an amplification attack - the attacker sends a request to a vulnerable third party server with the 'from' address of the victim. The third party sends out several packets to the victim. Scaling this up to multiple third parties means that an attacker need only use a little bandwidth to fill up a fat network conection at the victim.
I don't know where you read that udp was "faster". Its performance characteristics are very different from tcp (that is part of the reason that they exist as different protocols) but the speed of an ip connection is not simply a question of the bandwidth on the network hops between client and server. Attempting to send large volumes of udp packets across the internet and you will likely end up DOSing your uplink router.