there is usually a bus service running between the two airports. Cost I believe is 30rmb each, but do watch out for your timings. We used it earlier this year and due to the traffic congestion it took nearly two hours. So if your onward flight leaves fairly soon it may be better just to cough up for a taxi.

subway line 2 now connects both airports.  It's faster, hell of a lot cheaper, and more convenient than getting a bus

Subway is definitely going to be the cheapest way.  Less than 10 rmb for the trip in total.  Even though it's all on line 2, you do have to change trains once at Guanglan Rd.  Really simple, just walk across the platform from one train to the other....of course fighting against the sea of people transferring in the opposite direction, haha.  Overall travel time should be about 1.5 hours. 

If you have 50rmb to blow, and want to save yourself a few minutes, you can firstly take line 2 to Longyang Rd, and then take the Maglev to Pu Dong airport (or vice versa, depending on direction of travel).  Not 100% sure on the reasoning, but it seems during the daytime they will let her eat up to about 430 kph, but at night they slow it down to about 300 kph.  You should take it at least once, if just for the experience

I've never used the bus transfer, although I have a friend who swears it is much better than taking the subway (faster, more comfortable).  I guess it would heavily depend on the traffic.  At least with the subway there's no guessing on transit time, just guessing if you can find a seat or a space to call your own.  Gets damn crowded during peak hours.