I had used both Semi-Automatic as well as fully automatic washing machines. Both have relative advantages and disadvantages.
Generally we have 3-4 stages in any washing operation vs 1. soaking 2. washing 3. rinsing 4 Drying/ spinning
In semi-auto you have two tubs - one for Soaking, washing and rinsing and the second one for drying (by spin action). Hence the clothes have to be manually transferred from one tub to another after the washing/rinsing is over. In fully automatic all are performed in a single tub/drum hence no need for any manual intervention and transfer.
Generally most of the fully automatic washing machines have additional features and flexibility in setting a customized environment for the nature of clothes (wool/ silk/ light clothes/ heavy etc). Also some washing machines come with a facility of heating water to remove stubborn dirt. Also some washing machines have a provision for hot air circulation to make the drying more effective.
Generally the price of the fully automatic washing machine could be higher by 50% to 200% depending upon the model and manufacturer.
Some fully automatic washing machines take very high washing cycle time (1.5 hours to 2 hours) while some other take lesser time (45 minutes). Generally the semi-auto machines have a cycle time of 30 minutes to 1 hour.
Overall the washing quality is slightly better in fully auto machines. They also come with a provision to add bleach/ starch etc. This may have to be done manually in the semi-auto (depending upon the model).
My personal experience is that the fully automatic machines same quite a lot of time and effort. It is definitely worth spending some additional money to save lot of time and also to avoid mistakes.
If budget is not a constraint, fully automatic washing machines are a boon for time-constrained people - fill it set it, shut it & forget it till the washing is over.