I would say there are differences, but would tend to say do it the way you feel more comfortable with.
I have used both approaches, and having jQuery calls from the page is generally faster. I write an ashx handler that does the job the jquery call needs (query the database, process something, etc.) and call it from the page. I wouldn't use an aspx page for a jQuery call, because you're sending a lot of info that you won't need at all. The difference/ benefit of using an Ajax.Net call is that you don't need to build another page to process things, you can use the same page events to do it.
For example, if you need to fill a second drop down list using the selected value on a first one, you could use Ajax.Net to call the SelectedIndexChanged in the page code behind and when it fires go Page_Load, SelectedIndexChanged, Page_PreRender and so on. In the event method you'd query the db and fill the second ddl.
With jQuery that could be a bit different. You make your call to an ashx handler, the handler is just a server method that do the magic and return data in the form you want to have (json, array of strings, xml, etc) and fill the second ddl using javascript.
As I told you before, some people doesn't feel too mcuh comfortable with Client code and tend to do it in the server, but I always say that you need to use the correct tool for the right job, so know your tools and apply them wisely.
If you want to know more about ASP.Net, ASHX handlers and jQuery, you can read a post that I wrote about it.
Hope it helps.-