train vs bus, London to Portsmouth?

I think you answered your own question. The train is faster but pricier; the bus is slower but cheaper. If saving money is more important than saving time, choose the bus. Do check if discount train tickets are available (they often are, as long as you're buying sufficiently in advance and can live with non-refundable and non-changeable tickets). Sometimes, discount train tickets can match bus fares.

Robin,
I recently bought advance purchase train tickets (good for any time, any train on the day of travel) for £27.90 per ticket from Victoria Station to Portsmouth. I bought them at virgintrains.com. It is on Southern Rail. I didn't price bus fare. Trains also leave for Portsmouth from Waterloo station and are faster, but they cost more -- or at least they did for my search. Maybe this is useful for you.

The anytime fare is £27.90 for Southern Trains and £33.10 for all trains. If you travel after 9am or at the weekend the Southern fare is £26.90. There are advance fares on Southern tied to a specific train for as little as £5, subject to quotas.

We used www.aquacars.co.uk. They will fetch you from anywhere in London and deliver you to anywhere in Portsmouth, door to door, for less money than two train tickets. If you're alone it may not be worth the money. They met us at Heathrow and took us to our waterfront hotel in Portsmouth. Worth a look maybe. The door to door convenience was worth it to us.