Kalman Filter Sensor Processing Kalman filter achieves convergence of state vector by using sensor observations.

Assuming a sensor such like velocity sensor, giving two axis velocity information in X-axis as well as Y-axis(see edit for one more example to capture essence of my question)

I can always design kalman filter in such a way that X-axis and Y-axis velocity are taken as two different scalar sensor readings and also a kalman filter where I take them as a vector sensor reading.

From both theoretical and practical aspects Is there any thing I am losing by taking X-axis and Y-axis as independent readings? 

Or taking them together helps in converging faster? 
What is a better approach? And Why?

Edit: Assume one is in a airplane and a camera captures an image and tells latitude and longitude of nadir. With this data I would like to correct my State vector. Now if I use latitude as a different reading and longitude as a different reading than using both of the data. Will I lose anything? As pointed by an answer below if the signal model has an interaction among the components of reading I lose that interaction. Now do latitude and longitude have an interaction? How do I capture this interaction mathematically with H matrix?
As with any question like this, the answer is: It depends.

What does it depend on? Your signal model.

If your signal model generates $X$ and $Y$ axis velocities independently from each other so that there is no transfer function between the two channels, then two 1D Kalman filters will work the same as one 2D Kalman filter.

If your signal model allows interaction between $X$ and $Y$ axis values, then you lose that captured interaction between the axes, which can degrade the performance of the two 1D Kalman filters over a single more accurate 2D Kalman filter.

To give any more detailed answer will require you to state your signal model.



The edit really doesn't give me enough information, but let me try to update my answer.

I'm assuming, from what you say, that the latitude and longitude are estimated from a nadir image.  If that's true, then unless the image pixels are precisely aligned with the lines of latitude and longitude, you will get cross-coupling between your latitude and longitude estimates.

That cross-coupling means you'll be better off using a 2D Kalman filter.