First of all let look at the differences between them. Lawn vacuums or sweepers, as they are sometimes called, come in three varieties; hand powered, powered (gas or electricity) and towed. Leaf blowers come as only gas or electricity powered.
In essence although they are both to collect up unwanted leaves they each go about it in a very different way. The lawn sweepers, as the name suggests, is effectively a rotating brush that passes over the lawn and sweeps debris in to the collect bag. The leaf blower passes blows leaves and debris in to a manageable pile for you to do something with.
You may think – well no thoughts required here, I'll get a leaf sweeper – it takes a step out of the whole leaf collection process. With the blower I have to walk all over my lawn only to then have to pick the leaves up in the end, whereas with the lawn sweeper I can walk over my lawn with it and it collects the leaves in a bag which I can then neatly empty to wherever I choose. To a certain extent you would be right to think this, but then it really does depend upon the style and size of your lawn. For examples, there will be some lawns that are a very awkward shape that has a lot of nooks and crannies. It would be very difficult to get the lawn sweeper in to all of these and perhaps the leaf blower would be a better option.
Many leaf blowers have one function and that is to blow leaves, lawn sweepers can have many functions and uses. Not only can they be used for collecting leaves but you can also use them on your patio, driveway or any other surface that has debris on that you may want to collect. Some lawn sweepers also have a shredding facility; this is great if you want to create leaf mould or mulch for your garden. The shredding facility does have draw back though – you are not going to be able to use your vacuum on any other surface than grass. The shredder will not last long picking up grit of the driveway.
In terms of which is best for you, you need to look at the shape of your lawn, consider how much leaf fall you get and if you regularly sweep other non-grass surfaces.