Hi Bridget,
Let me preface this with a caution: I would guess I'm probably in the minority in my opinion. Keep in mind that this is JUST my opinion. Your/your clients' circumstances could mean a completely different view.
I moved to Office 2007 several months ago after working in open-source software for the last three years. Before that, I used Office 2003, and before that 2000, 97, and DOS versions.
I do Excel and PowerPoint sometimes, but I work primarily in Word, so I'll address that one first. So far, I've not found any advantage of Word 2007 over Word 2003. Both offer the same commonly used features and options including flexible and customizable page layouts; flexible typefaces and styles; custom tables, charts, and graphs; and easy to use auto-formatted elements like page numbering, headers, footers, and table of contents. And, unfortunately, 2007 still carries some of the same formatting and multiple-user glitches that every earlier version of Word had, too. So you likely won't find any surprises there.
I know lots of people who LOVE the 2007 "ribbon" interface, so don't let that scare you away. But I personally have found it hard to grasp. To me, the categorization of the options is not anywhere near as intuitive as it was in 2003. But on the other hand, the ribbon is set up in Excel and PowerPoint pretty much the same was as it is in Word, so once you find your way around one, you'll know them all. There's no re-learning a second and third time to understand the whole suite. Again--not much different from previous versions in that respect.
Compatibility can be an issue in 2007, much more so than in previous versions. 2007 encourages you to save in the new file format, which is NOT readable by earlier versions. This is very important to know if your clients are using 2003. The simple way to get around that is to always choose to save in the "97-2003" format instead of using the new format. The not-so-simple thing is remembering that the first few times.

But one thing that makes it easier is that in 2007, there is no automatic saving option. It ALWAYS asks you to choose which file format you want.
If you use 2007 and your clients use 2003, you will have no trouble opening client's files and, as long as you choose the same format, the client will also have no trouble opening yours.
I'm still learning 2007, so this is something I hope to conquer (perhaps because I don't understand it correctly yet). But for now, I find it frustrating that certain options are not available when I choose to use the older, compatible file format. For example, new documents can be saved as 97-2003 compatible files, but NOT new templates. Templates default to 2007, and a warning window pops up every time telling you some formatting may not translate correctly. Also, some of the form field features are only accessible in 2007 if your file is saved in the new format. Again, I may not quite know the ins and outs of that yet, but at the very least it is a learning curve detail you might want to keep in mind.
And like every new version of every program I've ever used, Office 2007 is an absolute resource hog compared to 2003. But since large-capacity memories are common in newer computers, this may not be something you notice much.
One last thing: if you decide to stay with 2003 a little longer but your client sends you a 2007 file, don't fret. You can convert the file through
Zamzar.com. It's free and accurate and does lots of other file conversions, too, not just old and new MS files.
And if you do upgrade, be sure to get a book or two to help you navigate the change. I like
Office 2007 for Dummies, but there are others also.
I hope that helps just a little.