I have started to read more about ECDH/ECDHE and am wondering if it has the similary issues as RSA - i.e. the processing power required for the decryption of private key is more than of the public key. If so, then are there are hardware accelerators available for these ciphers. I did not find them by a google search and so posting this here. Thanks for any inputs
You do not "decrypt the private key", you "use the private key for decryption".
ECDH is not an asymmetric encryption algorithm but a key exchange algorithm. Key exchange algorithms are like asymmetric encryption algorithms in which you do not get to choose the message which is encrypted -- but that's just as fine when you just want to establish a shared secret value, to be used for symmetric encryption, as is the case in SSL/TLS.
In ECDH, each involved party will compute two equivalent operations, which, on elliptic curves is the multiplication of a curve point by an integer. A simple PC, using a single core, has enough computing power to do that more than ten thousand times per second with the standard P-256 curve (which is as robust as you can hope for). This hardly mandates the use of an hardware accelerator: in HTTPS, such an operation will occur only once per client, when the client opens its first connection. Each connection will be used for several HTTP request, and extra connection will use the "abbreviated handshake" which use symmetric cryptography only.
You might want to do the ECDH and similar operations in some specific hardware, not for performance, but for security: private keys are sensitive objects, they are best kept in tamper resistant devices which will protect them from theft, even against local attackers. Such devices are known as Hardware Security Modules. When a HSM is used, the private key never leaves the HSM, and the HSM does the cryptographic operation. Some HSM support elliptic curves, e.g. recent Thales' nShield HSM.