STP (Straight Through Processing) (or NDD (NoDealingDesk))
means the broker will route your orders directly to the Liquidity provider, were the Liquidity provider becomes a Broker of the Broker and takes the other side of your trades, that does have the effect that liquidity is usually not an issue, but fills may differ some times.
ECN (Electronic Communication Network)
means the broker will send your order to a liquidity network build of multiple brokers, banks and other liquidity providers.
the Other side of your trades can be taken by other clients, or anyone that is connected to the same network, this has the effect that spreads are variable, but fills are far more reliable.
also, ECN execution has the advantage that you can manage fills more detailed, you have Depth of market (because you are in a real market) and it's usually more stable.
however the platform you executing on can make a major difference, if you as example using Metaquotes Software (MT4 / MT5) there is no such thing as ECN (even if claimed) the whole software suite is not designed and unable to manage partial fills or market management tasks, so using this platforms you always on a STP or DealingDesk system
the ECN is achieved by a ECN-Bridge which will send your STP order to an ECN pool, that's why you can get re-quotes even on an ECN connection because the initial command from your platform is done via STP where STP is not towards a bank but towards the ECN Bridge.
EDIT: there is no Better or worse when it comes to STP vs. ECN, both systems do have advantages and disadvantages, it is more about your trading style and size. STP as an example has a major advantage that the broker does know the liquidity before they send or while they do it. that can be an asset if the broker is on your team.
ECN on the other side allows for much larger Liquidity as it operates in a pool, but that can have the effect that you trade against clients of the same one (it almost always is like this) however that in itself has again an advantage since you get faster fills and less slippage.