What makes Portsmouth a more popular destination than Brighton for GWR? Is it simply they need to terminate a train somewhere and Portsmouth has lots of space?
There is a fair flow from Portsmouth to Southampton. GWR provide the fast service each hour while SWR provide the stopper. The current franchise was anticipated to add a SWR fast service with extension west of Southampton towards Bournemouth but I doubt it will every happen now.
Leaving the GWR services running to Brighton were fundamentally an Orcats raid. It would have made more sense from Southern to take them over and cut back the additional GWR services to Southampton.
Ignoring the random Bristol - Brighton services, going back to the end of 2002, the standard hourly service pattern was:
Wessex Fast Portsmouth - Cardiff
SWT Slow Portsmouth - Southampton
Southern Semi-fast Portsmouth - Victoria
Southern Slow Portsmouth - Brighton
Southern Semi-fast Bournemouth - Victoria via Hove
SWT Basingstoke - Brighton (extended to Reading every 3rd hour).
In 2003, the SRA mandated certain congestion relief measures (amongst others) with effect from May 2003:
The 2nd stopper from Waterloo to Portsmouth was cut back to Haslemere.
The West Croydon - Guildford SWT was chopped.
The Virgin XC services to Poole and Weymouth were cut back to Bournemouth, and
The SWT Reading services were cut back to Basingstoke.
The Southern service to Victoria was cut back to Southampton.
SWT ran Wareham - Brockenhurst shuttles which became Waterloo - Poole with long layovers in December 2007.
The December 2004, SWT "Know your numbers" timetable rewrite joined the stopping services across Southampton from London to Poole and introduced the second fast Weymouth but didn't alter much else.
In December 2007, there was a Southern re-write which diverted the Southampton / Portsmouth - Victoria services via Horsham. This led to
FGW fast Portsmouth - Cardiff
SWT slow Portsmouth - Southampton
Southern semi-fast Portsmouth - Victoria via Horsham
Southern slow Portsmouth - Brighton
Southern semi-fast Bournemouth - Victoria via Horsham
Southern semi-fast Southampton - Brighton
Southern slow Portsmouth - Littlehampton