Yes, there is a difference , and the longer the cattle are finished with grain, the greater the differences appears to be 
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. 
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.
 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.
 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.