You can practice in the US as long as you have a license. Board certification usually doesn't make any difference regarding license (this varies by state).
The main difference will be where you are working. Some specialty hospitals in the US (both private and academic) will hire only US-recognized specialists. For example, the job description will say something like "qualifications include diplomate status in the American College of Veterinary Surgeons" while others will say "ACVS or ECVS"
In general though, the European specialty boards are increasingly seen as equivalent to the American ones.
One other issue is whether your job involves training residents. Many of the American specialties only allow their own diplomates to train residents. But this is changing, especially considering universities are having a very difficult time recruiting and retaining clinical specialists.