Which is better for running?

The New Balance 1080 v15. It is a neutral road shoe with soft Infinion foam and a rockered ride built for daily miles. The Metcon 10 is firm and flat, which is uncomfortable over distance.

Which is better for the gym and lifting?

The Nike Metcon 10. Its flat platform, midfoot support bridge and studded outsole give stability for squats, deadlifts and rope climbs. The soft 1080 is unstable under load.

Can I use the Metcon 10 for running?

For short warm-up jogs and conditioning, yes. For regular road miles it is heavy and firm, so the 1080 is the better choice.

The Metcon 10 generally holds up longer in the gym, with a reinforced upper and tough outsole. The 1080's soft foam and knit mesh wear faster, especially on abrasive pavement.

Is the 1080 v15 good for wide feet?

Yes. It comes in narrow, normal, wide and extra-wide widths. The Metcon 10 comes in standard width only.

If you both run and lift regularly, yes. A soft running shoe and a stable training shoe cover different needs, and using one for both compromises each.

New Balance 1080 v15 vs Nike Metcon 10

These are not rivals; they are for different jobs. The New Balance 1080 v15 is a soft, neutral road running shoe built for daily miles and long runs, with a plush Infinion foam midsole and a rockered, flexible ride. The Nike Metcon 10 is a stable cross-training shoe with a flat, firm platform, a midfoot support bridge and a grippy outsole for lifting and gym work. Buy the 1080 for running; buy the Metcon for the gym.

Choose the New Balance 1080 v15 if your main training is road running and you want maximum cushioning for easy days and long distances.
Choose the Nike Metcon 10 if you lift, do CrossFit-style classes or mix strength work with short conditioning and need a stable, flat platform.

Prices

New Balance 1080 v15: $80.00 at eBay (last seen Nov 8)
Nike Metcon 10: $89.99 at eBay (last seen Nov 8)
Difference: the New Balance 1080 v15 is $9.99 cheaper than the Nike Metcon 10 at the latest prices (Nov 8)