Personally, I tend towards the flexible side. Perhaps that's an understatement. I have a goal in mind (Cape Town, South Africa), but that's about it. My basic plan is to ride from Ireland to Scotland (well, okay, I'll have to take a boat), then down through England, France, Spain, Morocco, Mauritania, etc., down to S. Africa. It's entirely possible, though, that I'll decide in France that I'd really like to see Norway, and then that I'd really like to see Poland and then Switzerland and then... you get the idea. I could bounce all over the map. My plans change on an almost daily basis, and occasionally as often as every five minutes. I don't particularly like the cold, so on this trip I'll try to get down into Africa by the end of summer/beginning of fall. It will be better to be passing through Morocco/Mauritania/Senegal/Mali in the winter, anyway (necessary, really, according to my research), so if I get there too quickly, it will be a bad thing.
Flexible scheduling has its share of problems, of course. First of all, unless you have unlimited financial resources (or some really cool sponsors!), you can't just travel forever. If your schedule is too flexible, it's easy to get stuck in one place, trying to see everything. It can also be hell for the people back home who are trying to keep track of you (my mother would gladly attest to this), particularly if they're trying to send you mail. My mother finally started making photocopies of any letter she sent me, so that she could send it to three different cities, in case I decided not to go to two of them.
A rigid schedule means that you will see what you planned to see, assuming that there are no unforeseen complications (plan on unforeseen complications). You will be able to pack much more into a limited period of time if you schedule it and follow your schedule. On the other hand, many of us prefer "quality" over "quantity."
Financial matters aside (since that may be the largest determining factor in your schedule, and if it is, you already know that), probably the biggest reason to go with a rigid schedule is to prevent strife within a group. See the end of the section on deciding whether to travel solo or with a group for a little more detail on that.