There are advantages either way when it comes to using the same or 2+ firearms for different purposes.
If you use the same gun, you should be very familiar with it, well practiced, and won't accidentally think to do something from a different gun that you don't do normally, or vise versa. It would be terrible to pull the trigger on your cocked&locked home-defense 1911 after forgetting about the manual saftey that your carry Glock doesn't have.
Having a second firearm can provide a larger, more comfortable option (with higher capacity, better muzzle velocity, etc) that you don't have to worry about lugging around all the time. Just be sure you are familiar with it and stay practiced.
Personally, I usually use the same gun for both; it just depends on which one it happens to be. I have several guns which I will carry and I rotate through them every few weeks or months. It just gives me all the more reason to take them to the range; I have to be well practiced with them! I've considered putting one of my larger revolvers in my quick-access safe for home defense for their ease of operation (I don't leave my auto's chambered when I take them off) but have not yet felt compelled to do so.