Id reccomend neither. Steam cleaning wont take stains or really bad smells out of the carpet. It only refreshes the pile of the carpet.

Dry cleaning - your dirt and dust is attracted to the chemicals that they put in your carpet as it hasnt been extracted. Youre carpets may end up dirtier.

I would reccomend an extractor (carpet shampooer) as it is the only thing that will take stains out and clean your carpet 100% without attracting more dirt and dust into the pile or ending up with mould etc

If youd like any more info please ask. I work in the cleaning industry and have just done my carpets also.

Good luck!