Nerve stimulation and ultrasound have been introduced to the practice of regional anesthesia mostly in the last two decades.
Electrical nerve stimulation has been an established method for localizing peripheral nerves. Electrical nerve stimulation in regional anesthesia is a method of using a low-intensity (up to 5 mA) and short-duration (0.05-1 ms) electrical stimulus (at 1-2 Hz repetition rate) to obtain a defined response (muscle twitch or sensation) to locate a peripheral nerve or nerve plexus with an (insulated) needle. The goal is to inject a certain amount of local anesthetic in close proximity to the nerve to block nerve conduction and provide a sensory and motor block for surgery and/or, eventually, analgesia for pain management. The use of nerve stimulation can also help to avoid an intraneural intrafascicular injection and, consequently, nerve injury.
Ultrasound did not gain as much popularity as the nerve stimulation until a decade ago because of the simplicity, accuracy and portability of the nerve stimulator. Ultrasound is now available in most academic centers practicing regional anesthesia and is a popular tool amongst trainees for performance of nerve blocks.1
Time and again the question arises whether in the long run ultrasound would end the era of electrical nerve stimulation. This is neither desirable nor to be expected.
Electrical nerve stimulation when used systematically, can achieve a success rate of approximately 90% .In addition, few references to persisting nerve damage from the use of nerve stimulation are found in the literature. The method is therefore absolutely well-established from the viewpoint of safety aspects as well. So the simultaneous use of ultrasound and nerve stimulation provides the less experienced user with an additional means of identifying nerve structures. 2
Also the combination of difficult anatomic conditions (e.g. massive obesity) and a deep block (e.g. a psoas block, or proximal sciatic block) can make it difficult even for the experienced ultrasonographer to display the target region, thus requiring additional use of a nerve stimulator to provide certainty. The motor response (twitch) to PNS is objective and reliable and independent from the patient's (subjective) response. Nerve stimulation is often helpful to confirm that the structure imaged with ultrasound (US) is actually the nerve that is sought. This is because the needle-nerve relationship may not always be visualized on US; an unexpected motor response can occur, alerting the operator that the needle tip is already in close proximity to the nerve.
Although existing studies suggest that the time required to perform peripheral nerve blocks is shortened with the use of ultrasound, the time required to perform an initial ultrasound exam is not included in the total time reported in any of these investigations2,3
In summary, without discounting the advantages of adding ultrasound guidance to the armamentarium of regional anesthesia, it would be fair to state that based on the current literature, ultrasound does not replace experience and knowledge of relevant anatomy, especially for visualization of deep structures where electrical nerve stimulation can be of immense help. In certain scenarios, ultrasound may not
offer additional value and substantial amount of time may be spent trying to find relevant structures. In other cases, it may provide a false sense of security, especially to an inexperienced operator.1

In summary, ultrasound and nerve stimulation from my point of view are not competitive techniques but rather enhance each other.

References:

1. Wadhwa A et al. Ultrasound Guidance for Deep Peripheral Nerve Blocks: A Brief Review.  Anesthesiology Research and Practice, 2011, Article ID 262070, doi:10.1155/2011/262070
2. http://www.nerveblocks.net/index.php/en/fudamentals/sonography/256-combined-procedure-dual-guidance
3. http://www.nysora.com/regional-anesthesia/3010-electrical-nerve-stimulators-and-localization-of-peripheral-nerves.html