All I can offer is my personal preference because there is no right or wrong answer to this highly subjective question. My preference would be to get a larger stone from another source, as this is what I (well, actually my now husband) did. My husband did months of research and ended up buying my diamond from Whiteflash. We picked out the stone together which had specs the same or better than what is offered at Tiffany. We then had Ritani custom make a setting for it. Shortly after getting the ring, I went to Tiffany and looked at their rings and was honestly happier with mine, especially when I looked at their price tags! This experience made me feel really thankful for such a wonderful husband who spent so much time and effort trying to get me the perfect ring at a great price which meant more to me than having a name brand.
With this said, everyone is different and has their own preferences. I completely understand that if the name and some of the other perks which go along with buying from a name brand are important, then that is what you should go for. If you buy a bigger ring, but will constantly long for a Tiffany ring, that is probably what you should get. As others have pointed out, you should do research, try a bunch of rings on, and decide what makes you happy and fits within you budget. Good luck!