Cycling pluses:
Cheaper
More enjoyable
More reliable
No timetable/hours of service
Usually quicker, around London definitely, longer journeys less so.
Learn more and see more of your surroundings
Potential to explore and do off the cuff detours
Positive mental health and buzzy exercise endorphins
Legs and buns of steel, and I'm less fat than I otherwise would be.
The great British public can be easily ignored/avoided if you wish.
Cyclists are mostly awesome and look out for each other, its like being in a club, even if you're not in a cycling club
Cycling cons;
Selecting the wrong clothing choices for the weather that happens can result in getting soaked and cold.
Form attachments to bikes so I don't want to sell them, resulting in much less space in my flat for other things
The expense of keeping multiple bikes on the road
eBay addiction, to try and reduce costs of the above
Can't buy trousers online, need to try them on first-see legs and buns of steel point listed earlier.
Lemming peds on phones and drivers on phones with a total disregard for their safety and yours
Crashing, it usually always hurts, and recovery takes longer the older you get
Bike thieves and indifference to bike crime as its low level. And related the sad fact any nice bike cannot be locked outside in London in confidence that it and/or its parts will still be there when you get back, even with good locks.
Cycling long distance makes you seem a weirdo to some people, I'm too old to care about this and I think couch potatoes are the weird ones
Trains pros
I can cover more than 200 miles in a day, if the trains actually work.
Less care needed with clothing choices and weather checking
If your bike is broken and you have no car or other means of transport, then the train is an option.
Nothing else
Train cons
Expensive, prices vary hugely across operators and certain times/dates
Unreliable, the longest list of excuses for poor service known to mankind!
Pathetic amount of cycle spaces on most trains
Utterly disjointed service since privatisation
Some operators you cannot reserve a bike space online
The great British public are on it, erggh.
If you're on a Virgin train the whole carriage which contains the toilet stinks of urine.
The food is awful and is a rip off
In summary bikes rock and trains suck.