Won't make much of an impact on First in Bristol, as seems to be acknowledged in Stagecoach's statement. Megabus is a different matter,and has virtually no direct First opposition. If First started selling depots, etc, to Stagecoach in Bristol or surrounding areas it would signal they were leaving the U.K. bus market!
This follows on from Stagecoach's acquisition of Wessex Bus in the same area and is a good bolt-on to the Stagecoach West business.
South Gloucestershire have been operating Megabus services since they parted company with National Express a couple of years back so effectively those services will now be run "in house".
I doubt Stagecoach will embark on large-scale direct competition with First on commercial services in and around Bristol, but will certainly give them a run for their money when it comes to contracted services.