Generally you're going to get less velocity because there is less area for the gas pressure to push on. Pressure in the barrel would be about the same using optimum powder. But the bullet has less cross sectional area for that pressure to act on. The difference won't be much if you compare something like 7mm to 6.5 mm. But if you compare 224 or 6mm to 7mm or 308, the difference begins to add up.
For long range you also need to factor in bullet SD and effects on BC of the bullet. That gets more complicated. But in general I still think you generally come out ahead with the larger bore unless you are talking a small case. For long range you need to factor in caliber, bullet weight, case size, and available bullets.
If you could give some idea what two calibers and case size you are considering, you might get a better answer.
