I recommend that you vary your choice of seeds and include different types of seeds in your Healthiest Way of Eating. Both flaxseeds and chia seeds are nutrient rich. They are both known as concentrated sources of the omega-3 fatty acid, alpha-linolenic acid (ALA). According to the U.S. Department of Agriculture's SR19 Nutrient Database, one ounce of flaxseeds contains about 4.7 grams of ALA while one ounce of chia seeds contains about 5 grams.
Both chia and flaxseeds are rich in dietary fiber: one ounce of flaxseeds contains 5.6 grams while the same amount of chia seeds contains 10.7 grams. Like all seeds, both chia and flax contain significant amounts of minerals, and they also both contain a variety of vitamins as well. Because they are very small seeds that we typically don't eat in large amounts, chia and flax do not provide us with large amounts of protein, even though they do contain a good bit of protein in relation to their size.
At this point in time, researchers have looked more closely at the nutritional profile of flaxseeds than the profile of chia seeds. For this reason, we know that flaxseeds are concentrated sources of lignan phytonutrients, which have antioxidant and other properties. There have also been some animal studies showing potential benefits of flaxseeds (or lignans obtained from flaxseeds) for the health of the prostate gland and some human studies showing possible benefits for the cardiovascular system. However, the extent of these benefits in humans remains a matter of controversy and debate. (It's the extent of the benefits that remains unclear in these studies—not the nature of the flaxseeds as a beneficial food). Although there has been less research with chia seeds than with flaxseeds, I would expect potential benefits (and perhaps some controversy) with respect to these seeds as well.
For more information on this topic, please see:
Bloedon LT, Szapary PO. Flaxseed and cardiovascular risk. Nutr Rev. 2004;62(1):18-27.
Dupasquier CM, Weber AM, Ander BP, et al. Effects of dietary flaxseed on vascular contractile function and atherosclerosis during prolonged hypercholesterolemia in rabbits. Am J Physiol Heart Circ Physiol. 2006;291(6):H2987-96.
Hallund J, Ravn-Haren G, Bugel S, et al. A lignan complex isolated from flaxseed does not affect plasma lipid concentrations or antioxidant capacity in healthy postmenopausal women. J Nutr. 2006;136(1):112-6.
Hallund J, Tetens I, Bugel S, et al. Daily consumption for six weeks of a lignan complex isolated from flaxseed does not affect endothelial function in healthy postmenopausal women. J Nutr. 2006;136(9):2314-8.
Harper CR, Edwards MC, Jacobson TA. Flaxseed oil supplementation does not affect plasma lipoprotein concentration or particle size in human subjects. J Nutr. 2006;136(11):2844-8.
Kitts DD, Yuan YV, Wijewickreme AN, et al. Antioxidant activity of the flaxseed lignan secoisolariciresinol diglycoside and its mammalian lignan metabolites enterodiol and enterolactone. Mol Cell Biochem. 1999;202(1-2):91-100.
Kuijsten A, Arts IC, van't Veer P, et al. The relative bioavailability of enterolignans in humans is enhanced by milling and crushing of flaxseed. J Nutr. 200;135(12):2812-6. Paschos GK, Magkos F, Panagiotakos DB, et al. Dietary supplementation with flaxseed oil lowers blood pressure in dyslipidaemic patients. Eur J Clin Nutr. 2007 Jan 31.
Prasad K. Effect of chronic administration of lignan complex isolated from flaxseed on the hemopoietic system. Mol Cell Biochem. 2005;270(1-2):139-45.