Are the Thin clients Electrum and Multibit safe and secure? How do Electrum and Multibit compare for being safe and secure. Both are open source. Are there any advantages, security wise, to use one or the other?

I'm new to bitcoin and the only reason for considering these thin clients is to not having to maintain a 5gb database file.
Currently, Electrum is more secure than MultiBit as the MultiBit wallets are not encrypted. The next version of MultiBit, version 0.5.9, supports encrypted wallets. (Disclaimer: I am the lead MultiBit dev)

Security in Bitcoin is related to many things. Here are some of them:

1) Is the code open source and do the developers have a track record ?
Both Electrum and MultiBit are open source so you can inspect the code. They have both been developed by pretty much the same people for over a year now.

2) Can you verify that the download you get is the correct one ?
The attack vector here is that an attacker substitutes a trojan instead of the real installer.
The MultiBit installers are all downloaded from a dedicated server via HTTPS and are signed with my PGP key. You can verify this after you download the installer (but before you run it). As long as my private key is not compromised this means only I could have signed it.

I am not exactly sure what Electrum does about signing its builds but I know Thomas (the lead Electrum dev) is very conscious of this area/ attack vector.

3) Are there any servers that can steal your bitcoin ?
MultiBit uses the regular Bitcoin network and they don't have your private keys. Electrum uses (many) of its own custom servers but again these do not have access to your private keys.

4) Both clients are theorectically open to an attack if their network connection is owned and the attacker can feed them completely false information. 

5) Both clients (well every client in fact) would be vulnerable to keyloggers capturing passwords which (in combination with the encrypted wallet in MultiBit's case) would give an attacker access to your private keys.

tl;dr At the moment Electrum is more secure. When MultiBit supports encrypted wallets they will be comparable. Good security practices on your machine are also important to keep your bitcoin safe.