Diffie Hellman and RSA are both asymmetric key algorithms, also known as publickey cryptography system which uses two keys to encrypt a plain text.
Diffie Hellman(DH) 
RSA 
DH stands for Diffie Hellman  RSA stands for Rivest, Shamir, Adleman. 
First published in 1976  First published in 1977 
Diffie Hellman was designed by Whitfield Diffie and Martin Hellman  RSA was designed by Ron RIvest, Adi Shamir, and Leonard Adleman 
Allows two parties to establish a connection over an insecure communication channel, a shared secret key that only the two parties know.  In RSA, the sender encrypts the data using the public key and the receiver decrypts the data using his private key. 
Generating ephemeral keys for Diffie Hellman is extremely easy  Generating ephemeral keys for RSA is extremely difficult 
Encryption is expensive  Encryption is cheaper 
Diffie Hellman 1024 bits is more robust than RSA  RSA 1024 bits is less robust than Diffie Hellman 
Publickey is bigger to encode  Publickey is smaller to encode 
Diffie Hellman is less secure than RSA  RSA is more secure than Diffie Hellman 
Also read: Difference between AES and DES in cryptography
Advantages and Disadvantages of Diffie Hellman
Advantages of Diffie Hellman

Sharing of secretkey is safe.

Sender and receiver don’t need any prior knowledge of each other.

Once the keys are exchanged the communication of data can be done through an insecure channel.
Disadvantages of Diffie Hellman

The algorithm cannot be used for signing digital signatures.

The Diffie Hellman key exchange is susceptible to maninthemiddle attack.

Only used for symmetric key exchange.
Advantages and Disadvantages of RSA
Advantages of RSA

Easier to implement and understand.

RSA is stronger than other symmetric key algorithms.

RSA has overcome the weakness of symmetric algorithms i.e. authenticity and confidentiality.

Very fast and simple encryption and verification.
Disadvantages of RSA

RSA has too much computation.

It requires a more computer power supply compared to singlekey encryption.
Protocols that use DiffieHellman to enhance security

Transport Layer Security (TLS) / Secure Socket Layers (SSL)

Internet Protocol Security (IPSec)

Secure Shell (SSH)
What kind of attack is a standard DiffieHellman key exchange vulnerable to?

Maninthemiddle attack
Keep it up, nice post! Exactly the info I needed to know.
Glad it helped!!
Youre so right. Im there with you. Your weblog is definitely worth a read if anyone comes throughout it. Im lucky I did because now Ive received a whole new view of this. I didnt realise that this issue was so important and so universal. You absolutely put it in perspective for me.
This article is awarded a 2 thumbs up from me.
I really like your writing style, wonderful info , appreciate it for putting up : D.
Thanks!!!