Yes, there is a difference [1], and the longer the cattle are finished with grain, the greater the differences appears to be [2]
Grass-based diets have been shown to enhance total conjugated linoleic
acid (CLA) (C18:2) isomers, trans vaccenic acid (TVA) (C18:1 t11), a
precursor to CLA, and omega-3 (n-3) FAs on a g/g fat basis. While the
overall concentration of total SFAs is not different between feeding
regimens, grass-finished beef tends toward a higher proportion of
cholesterol neutral stearic FA (C18:0), and less cholesterol-elevating
SFAs such as myristic (C14:0) and palmitic (C16:0) FAs. Several
studies suggest that grass-based diets elevate precursors for Vitamin
A and E, as well as cancer fighting antioxidants such as glutathione
(GT) and superoxide dismutase (SOD) activity as compared to grain-fed
contemporaries. Fat conscious consumers will also prefer the overall
lower fat content of a grass-fed beef product. [1]
However, in the amount of meat that one might ordinarily consume and with the normal food preparation of removing visible fat, the effect on your health may not be that much different. I don't think the hypothesis that grass fed is better (or less bad) for cardiovascular health has been tested in prospective trials yet.
[1] Daley CA, Abbott A, Doyle PS, Nader GA, Larson S. A review of fatty acid profiles and antioxidant content in grass-fed and grain-fed beef. Nutr J 2010 Mar 10;9:10. doi: 10.1186/1475-2891-9-10. PubMed PMID: 20219103.
[2] Ponnampalam EN, Mann NJ, Sinclair AJ. Effect of feeding systems on omega-3 fatty acids, conjugated linoleic acid and trans fatty acids in Australian beef cuts: potential impact on human health. Asia Pac J Clin Nutr. 2006;15(1):21-9. PubMed PMID: 16500874.