Jaggery is much less sweet than white sugar - the extra compounds and flavors take up about a third as much space in jaggery (jaggery needs a third to a half more to sweeten by a similar amount, depending on the properties of the batch). It also contains more moisture than white sugar, up to 20%, and is hygroscopic - it will pull moisture out of the air and become softer. Between the two, jaggery is bulkier, softer (semi-solid, usually), and moister than white sugar, which is dry hard crystals.
For many recipes, this difference in sugar volume or moisture might not make too much of a difference - but you will have to keep an eye on descriptors in the recipes, and watch for textural differences, like a batter or dough being the wrong consistency (too dry or too liquid) for having more volume of one ingredient, or something not mixing quite like the recipe says it should. Recipes with high proportions of jaggery will also tend to soften over time, because of its hygroscopic nature (gaining moisture from the air). You should be able to tweak things back into order if it's just a mechanical difference while cooking, recipes often can take little adjustments, but be aware there might be differences because of it that can't be worked around in more tightly balanced recipies.
Also, some techniques will be a little more difficult - for example, creaming butter and sugar together is a common technique, which takes advantage of the sugar crystals and their physical properties. It is possible to cream brown sugar, so using jaggery might be possible as well, if it is fairly dry, and well grated. However, you should be aware of the potential difference.
As to flavor, jaggery still has the flavor compounds that in white sugar, have been washed out to make molasses. Jaggery has an earthy, caramel or toffee type flavor on top of the sweetness, while sugar has a simpler single-minded sweet taste. It isn't a bad flavor, I quite like the flavor profile, but it may compete with other flavors in a recipe in a way white sugar just doesn't.
For most recipes, the end result will be a different, but not necessarily bad. If you do run across a recipe where jaggery just isn't working, and you aren't willing to resort to white sugar, you might try other sweeteners (like honey, or brown sugar) which will have their own flavor variations and chemical properties, but which may also be common enough to find a similar recipe that already accounted for those differences.
You could also look into what's marketed as raw sugar, something like turbinado or demarra sugar. These sugars are physically more like white sugar - they come in dry, hard crystals, and measure much closer to white sugar, although they are darker (golden to golden brown), and the flavor profile has some of the same caramel notes found in jaggery. They really aren't the same as jaggery at all, for all they are called "raw", but they might be an acceptable substitute for very picky recipes since they have crystals that act more like white sugar.