Only advice I can give is look before you leap. I switched from private sector – oil industry with 36-48 hr days (start job, keep working til you finish) and have now done various flavours of public sector.
You don't say which bit of public sector you are moving into and it's a big place with plenty of variation – civil service, nhs, local authority etc etc. I work for a metropolitan council and we're a loose conglomeration of at least 100 'small businesses'
Also in my experience the 'perks' are disappearing fast. Job security – 2000 redundancies at Birmingham city council, good pension – not for much longer if you believe the papers, steady salary – pay freeze this year with 3% inflation and single status may take a chunk, training – we're on no non-essential spend, it's been decided training is non essential.
Work life balance can be better but might be worth asking the questions above?