Control of either is similar. Once established, they can be very difficult to control. Mechanical removal of plants and roots will eventually suppress the population but will take constant vigilance. Mowing and cutting alone can promote root sprouting and are therefore not recommended.

Usually, the best approach for controlling larger infestations is to cut the stems and treat the stumps with a coating of a herbicide such as glyphosate (Roundup Weed and Grass Killer Concentrate, among others) or triclopyr (Bayer Advanced Brush Killer Plus).

Both of these herbicides can cause injury to other vegetation, so your product choice may depend on what you have closest the base of the stumps. Glyphosate will kill or injure any plants with which it directly contacts green tissue, green bark, or exposed roots. Glyphosate is probably the environmentally safer option because it has no residual activity. Triclopyr will impact broadleaf plants and trees if it comes into contact with them, but it may be slightly more effective than glyphosate. Triclopyr will persist for a short period of time and restrict some replanting for around 30 days (see label for details). As with any herbicide application be sure to read and follow all labeled directions.

If there is visible water nearby a permit may be required. Contact the MI Department of Environmental Quality (DEQ) Aquatic Nuisance Control Program Staff at<personal data hidden> for more information. Also, a list of approved aquatic herbicides needs to be consulted on the MI DEQ website (https://www.michigan.gov/documents/deq/wrd-anc-approvedherbicides_445623_7.pdf ).  

The timing of control is best done prior to the development of new seeds. If a second treatment is needed during the same season, late-August to early-October is a good timing as resources in perennial plants are being stored in the roots at that time in preparation for winter.

There is a good informational sheet available from the MI DNR that you may find useful at https://mnfi.anr.msu.edu/invasive-species/OrientalBittersweetBCP.pdf