The biggest issue would be budget. But probably best to keep it same if possible, rather than mismatching materials.

Carpet is probably easier and cheaper. Fresh carpet looks great and will give years of service with regular cleaning. Choose something that suits the house and it's style.

applepie, we just replaced our carpeted bedrooms with a very good quality laminate, like you the carpet was just awful and we wanted something that would last much longer this time. Our tiles are creamy white and they are in all the 'living' areas, the laminate planks are a rich red brown and look beautiful next to the tiles and rich creamy white walls. We inverted the design somewhat, cream tiles with rich red brown furniture in the living areas, and rich red brown flooring with creamy white furniture in the bedrooms. Here's a pic of our study ...

It probably depends a bit on the layout of the house. If the areas you want to replace with floorboards are closed off to the more open plan/walkway areas that are tiled then I think that would be ok. Is your carpet very similar in tone to the tiles or is it quite distinct already where the flooring type changes? Another option might be a very easy to maintain, durable carpet in the living areas and a same-toned plusher version for the bedrooms. Kids and their toys tend to scratch and dint floorboards (I personally just accept this as giving it 'character' ) and they do love a comfy carpet or rug to play on. Ultimately do what works and is practical for you and your household.