Which lens would need a polarizing filter more? A wide angle or a Zoom lens?

I'm on a limited budget. I have a Nikkor 18-55mm lens and a 55-300mm lens. The 18-55mm has a diameter of 52mm and the other has a diameter of 58mm. Both polarizing filters are the same price.

Can anyone tell me which filter would be more useful for me?

Which ever lens you use more, buy the filter for that, if your budget allows only one filter.
You can also check out non-nikkor filter. Hoya is one option.

You could invest in one of those step-up adaptors and use the 58mm polarising filter with both lenses. It might also come in useful for any other filters you decide to buy in the future (saves getting two of everything). They're cheap as chips…

http://compare.ebay.co.uk/like/170662255089?var=lv<yp=AllFixedPriceItemTypes&var=sbar&adtype=pla

Buy the big one and get a step-ring, then you can use on both lenses.

Get the filter for the larger lens, then get a step up adapter for the smaller lens.

The adapter is cheap. It is only around $15, as opposed to $300 for a quality polarizing filter.