how2girl is right, ducted is better. Ducted extracts better and with less maintenance. But it might be difficult or impossible to do, for example in a two storey house with the kitchen in the middle so that there is nowhere for the ducting to go. suzineedsahouse is right, different people have different requirements and what is important for one person might not be important for another person. I have seen a house where a window beside the cooktop was enough for the owner (I did wonder how that works on windy or rainy days). Some people are happy enough with a non-ducted rangehood. Some people insist on a ducted rangehood and are willing to rearrange their houseplan if necessary to ensure they have space to install one. I have heard of people who have chosen commercial rangehoods for their home. I know of people who have a second kitchen outside in their alfresco area which they prefer to use for some of their cooking and sometimes even those have a ducted rangehood. (Btw as far as I know a gas cooktop only affects your choice in regards to how high above the cooktop the rangehood must be.)

You can get slim range hoods that generally fit into the wall cabinets ours were approx 40cm deep which housed the complete operation, our plumber ran a 6 or so inch flexable ducting into the roof cavity and out under the eaves. Most brands make these. A photo would be helpful. https://www.thegoodguys.com.au/omega-52cm-undermount-rangehood-oru50x?CAWELAID=620013790000422290&CAGPSPN=pla&CAAGID=21711678566&CATCI=pla-376401441757&gclid=CjwKCAjw0qLOBRBUEiwAMG5xMNN63iJr0n0Bnxf31-Gt0t5s0vERt_lOwOYkC6uzovf9TDWwawry9RoCgxQQAvD_BwE&gclsrc=aw.ds&dclid=CLOv9erawdYCFc0slgodE5oLHg Where we didn't have wall cabinets we had tall boxes of stainless look laminate built up to the ceiling which contained the extraction unit, which was approx 30-40cm's and extraction ducting cheers

My family is looking to buy a new range hood. Ours right now is just too weak, it doesn't really suck air out. What do you guys/gals recommend? We've looked around and saw this one: Broan 413004 ADA Capable Non-Ducted Under-Cabinet Range Hood Do you think it's good? Any opinions? Thanks!

For the small amount of range hood that would be in contact with the undulating subway tiles, I do not see a problem.