I have had Photobucket for years but I chose to use Zenfolio for a few reasons.
First, a site like Zenfolio allows a lot more control over what you can do with each image. For instance, the Middle school soccer team shoot I did in February, was a mixed bag of goodness and frustrations.
There were 18 total parents. Two were "photographers" themselves and both were pissed that they didn't get the shoot. So those two didn't pay me for the session and did not order prints and did not get a copy of the images like the others did. Three of the remaining parents did not ever pay me even though they said they wanted the images and prints. All of the girls are friends and every one of them had several photos done with group (buddy shots) shots with other girls. Most of those group buddy shots contained at least one of the girls of the parents that didn't pay.
Using Zenfolio I was able to upload all of the images into the team shots folder, hide it so it is accessible from URL only, and then for security I am able to choose individually which photos can be downloaded or have prints ordered. Knowing some of the parents may be friends with the other parents, and might share the URL with others, I locked the images that contained the girls photo whose parents didn't pay me. They can see them but cannot download or order them.
I can also require each visitor to log in and leave contact information such as email and a name. I can then keep track of exactly who has visited and can email them from within Zenfolio.
Zenfolio now utilizes/stores/displays RAW images whereas Photobucket does not.
Zenfolio has a good many templates for website design and is really customizable to your desires.
I purchased my own domain name and Zenfolio allows me to point that domain to my Zenfolio account.
Zenfolio accounts start at $30.00 a year for basic that limits upload file size and storage space and no domain routing. The Zenfolio account I have costs $60.00 a year for unlimited upload size and unlimited space but prices are set at base lab prices for customers to order prints. For $140 a year you get a lot more stuff and can set prices to your images and make profit off the orders. I like the plan I have for the unlimited space and unlimited image file size.
What I am not happy with particularly are the vendor selections. Mpix is ok I guess and is the main print supplier for the US market. I would like to see Nations as a choice as well but not at this time.
So while I am a Zenfolio fan I am not saying it is the only choice but is the choice I made and I have no regrets.