Which is better the better choice?

I have an 18-55mm lens which came with the camera. I want to buy a telephoto zoom lens. After a lot of research i came up with the Tamron 18-250mm lens and Tamron 70-300mm lens (without stabilization).

What i like about the 70-300mm lens is the macro mode as a i like to take macro photos with my Nikon D3100 DSLR, the problem is that this lens is not versatile as the 18-250mm lens.
So should i buy the 18-250mm and sacrifice the 50mm difference and the macro mode? Or buy the 70-300mm and ignore the changing of lens?

Frankly I'd suggest you say with your camera brands lenses. Tamron is a 3rd party maker that I don't recommend because of the bad experience I've had with a product of theirs.

You didn't mention your camera maker but stick with them.

The better choice is always better. Between two better choices, one is always better than the other. You just have to find a way to determine which is better among better choices. Redundancy does have an effect on the betterness of some better statements.

The macro mode on the 70-300mm may not be what you want. Check the minimum focusing distance at macro mode. Optically, however, it's better than the 18-250mm. You may suffer however from the lack of an anti-shake feature.

Since your interest in getting a new lens is the telephoto end, I'd still recommend the 70-300mm. You will miss that 50mm difference.