Have to declare an interest upfront ... a few years ago I worked on the development of the product which was installed in AIB as transactonline.
I noticed also as of the time of the OP that the service was very erratic, indeed it seemed to stay that way until about a month ago. I've not had a problem since, and I'd use the service pretty much every time I shop online.
The main differences between Transactonline and "Web Shopping" would be as follows:
1) Transactonline: [broken link removed]
This basically gives you a computer program with which you can generate one-off substitute credit card numbers for use online or in any "card not present" type transaction. You generate the number up to a specified limit. That number is then valid for ONE transaction up to the limit you specified at the time you generated it.
The benefit here is that, having been used, the number is of no use to anyone else who might get their hands on it. You haven't given out your "real" credit card number, just a one-off pseudo random substitute number. Also, it could prevent being charged too much by mistake (if you set the limit appropriately for your transaction)
The substitute number is recognised by the bank when the transaction settles, and ultimately the transaction gets charged back to your regular credit card.
2) Webshopping (or Verified by Visa)
The difference here is that you do use your regular credit card number to buy online. At or about the time you check out your purchases, you are asked to authenticate yourself, presumably with a user/password combo (I have not used it myself).
The idea here is that you have to prove you are who say you are at the time of purchase. If your card is stolen, it would be less likely that your password etc. information would have been compromised at the same time.
However, Verified by Visa does require that the merchant has signed up to the programme and presumably has made changes to their website to allow it to work. It looks like you can get a list at this address:
http://usa.visa.com/personal/security/visa_security_program/vbv/shop.html
It therefore would be of little protection anywhere else, online or off!
Hope that helps.