I made some progress on this after chatting live with Eric from Digi support, and also reading around HOWTOs on the net.
First point is that the XBee 2.5 model is discontinued and no longer supported by Digi, even though it's still pretty widely sold. Eric mentioned that there are some better and more up-to-date models available, I think the 'ZB' line rather than the 'ZNet' is what you want. But I'm not completely clear on that yet (and I have the 2.5 which I wanted to get working).
Next, because the XBee 2.5 and XBee PRO 2.5 are no longer supported, the firmware is not available automatically from the X-CTU program. To get the firmware, you can still download it manually, and then use the 'File' option in the X-CTU download tool to get X-CTU to use the latest firmware. The firmware I needed was on this page: http://www.digi.com/support/productdetl.jsp?pid=3261&osvid=0&s=269&tp=2&tp2=0
Next, you can follow the information in the 'Xbee Configuration guide', see link at http://www.arduino.cc/en/Guide/ArduinoXbeeShield
You have to set up one XBee as 'ZNET 2.5 COMMUNICATOR AT' (the 'home base' xbee) and the other as 'ZNET 2.5 ROUTER/ENDPOINT AT' (the 'remote' xbee). You can assign names (ID) and network IDs (PAN ID) to both XBees using X-CTU.
Using this approach, the serial test worked OK, so it's looking good. According to Eric, what one should really be doing here is upgrading the firmware to the new 'ZB' feature set, for which instructions are here:
http://ftp1.digi.com/support/documentation/upgradingfromznettozb.pdf
I'm entirely sure why one should do that, other than to enable digi to support you better, because they don't actually support the ZNet modules, which apparently date from year 2006.
(1) Noe enough information provided.
(2) Too much happening. Probably.
(3) If "I am not able to repeat the same for the other module." means, "ever in amy circumstancve when operated in the manner which allows the other one to work", then if the two are identical parts with identical configurations then one is, by definition (more or less) broken. Or both are. Otherwise,
(4) Xbee shield is probably not broken.
Re 20 second issue:
If this happens with bad Xbee only then work that out first.
If it happens with "good" xbee then somewhere there will be a boundary. You need to find it.
Do the absolutely minimum necessary to get interaction with the shield that you can detect (LED on or supply present or some signal occurring.
THEN STOP.Let it sit. Does it "die" after or 30 seconds or one minute or more?
If not, work up in complexity from there.
If it does stop as before, work down in complexity and find what XBee directed activity (even with Xbee not being accessed) removes "stopping"
Best Answer
I recently used that same Xbee module in a project along with a pair of 6dBi omnidirectional antennas that while not identical look similar to the ones you've found and we got a range of 8 km line of sight but within an urban environment. It may have got further but geography limited how far away we could test and remain line of sight.
For that test one antenna was mounted out of the window of a house (not elevated above it) and the other one was mounted on a vehicle so roughly the same as your setup. A rough rule of thumb is that adding 6 dB of gain will double the range so you'd expect a pair of 6 dB antennas with a total gain of 12 db to have roughly double the range of the pair of 3 dB antennas with a total of 6 dB.
Using limited transmit power modules with large antennas does make sense although you can end up exceeding the legal radiated power limits for a band, however if you look at the end of the datasheet there's a list of FCC approved antennas and some exceed that amount of gain. But it's worth looking at that table anyway it might give you a few other antenna part numbers and styles to look at.
About the only other piece of advice I'd give is that for the best range it's worth keeping the antenna cable as short as possible, if you were to use a fairly average coax like RG-58 then 6 meters has about 3 dB of loss at that frequency so for example on the bus it'd be better to place the module right near the antenna and run back the data and power cables if possible.