What are the pros and cons of different methods for transferring Bitcoins between different wallet services? I am interested in transferring Bitcoins between several different wallets: my Mt.Gox account, my Bitcoin client wallet, and my Blockchain wallet.  I am aware of two primary ways to transfer funds between any two of these:


Perform a transaction from one address linked to one wallet to an address associated with the other wallet service, or
Export private keys from one wallet and import them on the wallet I wish to effectively transfer to.


I was wondering what pros and cons there are to these two different methods and if there is an obvious "right way" to do it?  Any other methods, ideas or advice relating to transferring Bitcoins between these wallet services would also be appreciated.  My primary concern is maintaining security, however ease of use would I think obviously be a nice benefit.
This is a very interesting question. Of course there is no "right way" and as far as I know not even a best practice. I can't make up for myself either what I'd consider the best method, but I'll list up some considerations.


Not all clients allow exporting and/or importing private keys. I think this will be the biggest problem when you decide to go for the second method. There are even wallets that don't store individual private keys for every user, but just store all the coins from all their users somewhere together (probably for a big part in safe cold storage) and just send some when you want to make a transaction.
Transferring private keys involves some risk. Any sort of malware can be operating in your computer to monitor the appearance of private keys. F.e. malicious browser plugins scanning web pages for private keys, spyware monitoring your clipboard and looking for wallet.dat files or network spoofers monitoring private keys included in unencrypted network traffic. 
Sending the coins over can cost you a transaction fee. This is normally no significant amount, but when sending much small amounts this can weigh. Of course you have to keep in mind that when you export-import the private keys, you will eventually pay the fee as well when you want to spend the coins.
When you want to transfer the coins to the wallet that will become your mail wallet, you may already have used its address on several places on the internet. When importing the private keys for other addresses will not make the coins available on your main address, but on the imported one. Most clients have no problem with sending/receiving from multiple addresses, but f.e. when you send coins with that other address to a contact that saved your main address in their contact list, they will not know that the payment comes from you.
The inverse argument of the previous one counts as well. If the address you want to move to another wallet is considered your main address (the one you shared with contacts), you will probably very much like to keep this address in your new wallet and importing it in your new wallet will be the very best option.
Just sending the money over is of course far easier than the hassle involved with transferring private keys. Some wallets f.e. don't allow you to import raw private keys but require them to be in some specific form like a wallet.dat file or some home-brew JSON format.


I hope some of my considerations help you to decide what to do with your two wallets.