I need to replace my ceramic cooktop which is ten years old, but now most of the cooktops within my budget have smaller elements, so my frypan will be larger than the elements. Does this matter?
Matching the size of pan to size of burner is the most important consideration for creating a cooking surface with even temperature. Parts of the pan bottom that reach beyond an electric element will not heat well at all and could remain a hundred degrees or more lower in temperature than the center of the pan, depending on the pan size and design. (Yes, I'm not joking -- I've measured such differences with an infrared thermometer.)
The folks who wrote the giant food-science book Modernist Cuisine did detailed tests and used computer models to determine what happens to heat distribution in pans under various conditions. (Here's a link to an abbreviated passage which deals with the issue, and this video has a number of their images showing the differences in heat distribution, including large vs. small burners.)
From the first link:
When it comes to heating food evenly... What matters more are the thickness of the metal, the size of the pan, and the size of the burner heating the pan.
Basically, they conclude that size of burner trumps just about anything else in terms of whether your pans heat evenly. The best way to counteract burners that are too small is to add thickness to your pan, or -- as they recommend -- to get a conductive thick metal plate made from aluminum or copper to put over your burner. That will help to spread the heat out a bit, though it will make your stove a lot less responsive, since it will take a long time for that thick plate to heat up or cool down. And it still won't be the same as a larger burner.
(As an aside, in the quotation above, I left out part of a sentence that says "the metal the pan is made from is the least important factor," since I think that's incredibly misleading. It's a combination of metal and thickness which determines the thermal profile. Modernist Cuisine's own research shows that to get the equivalent benefit of more evenness from an extra millimeter of copper, for example, you'd need to add about an entire inch of thickness to a pure stainless steel pan. From a practical standpoint, aluminum or copper are the only two materials where extra thickness in a pan to achieve evenness is actually feasible without creating a pan that would weigh several hundred pounds. Aside from pans using aluminum or copper in the base, there's little reason to shop specifically for extra-thick pans -- you'd be better off getting larger burners or getting a copper or aluminum plate to put under your other pans.)
A personal anecdote related to this -- A few years back I moved into a house with an electric cooktop, and I attempted a chicken-and-rice dish in my large oval enameled cast iron dutch oven. Despite having a rather large electric burner, the oval pot still stuck out over an inch beyond the burner on both sides. I figured water would circulate at a simmer. But I found out how much of a difference burner size makes: after simmering until the rice in the center was so soft it was starting to break down, the rice outside of the burner was still hard and crunchy. It wasn't even cooked. And this was in a dish with a lot of liquid that could potentially circulate around. Since then, I've discovered the only way to cook anything in pans that are larger than my burners is to move the pan/pot into the oven.
In sum: If you're only planning on doing slower cooking at lower temperatures in your large frypan, you may be able to get away with smaller heating elements if you stir periodically. If you plan to cook at higher temperatures (as you probably tend to do in a fry pan), you may have significantly greater difficulty getting things to an even doneness. A thick aluminum or copper plate under your pan might help, but it can only do so much.
Most likely, yes, it will matter.
Unless your frying pan is really super heat-conductive material or the size difference minimal, the outer areas will be significantly cooler than the middle. That's ok (but not ideal) for dishes that get moved constantly (think stir-fry), but when making something that fills the entire bottom of the pan (omelette), you are very likely to end up with either undone edges or a burnt middle - or both.
Keep looking for different tops. When you need uniform heat, you want the burner to be a bit larger than the pan bottom. This helps cancel the edge effect. However, most of the time I find that I don't need more than one large burner. Anything that is simmering it doesn't matter.
Get the stovetop with the largest burner you can find, then buy one new pan to match that burner if none of your existing ones work.