The GNER/NXEC system requires no major rollout of infrastructure, but is slower. Routers can be rebooted by on train staff or remotely, and it's the same system that I used in Sweden on the X2000. When you log in, you can even see on the 'home page' a map showing where the train is. It's satellite based, using mobile as an uplink I believe, and is relatively slow for what people might expect these days (watching BBC iPlayer, YouTube etc).
The other system uses a range of WiMAX base stations and 3G/2G coverage, and can be VERY fast. However, it is more expensive to roll out and has so far been used on Southern trains and Heathrow Express (where it works very well).
You can pay by credit/debit card, use a scratch card (presumably sold onboard) or bill it to your T-Mobile account by sending a text to a shortcode and getting a login. The latter is very easy if you're a T-Mobile subscriber (and some tariffs even include Wi-Fi for free).
Personally, with the roll out of 3G with HSDPA and HSUPA (high speed uploading and downloading), I think a laptop with an embedded 3G modem is probably better than sharing a Wi-Fi connection. The problem is that many trains have poor coverage, although that can be rectified with repeaters/leaky feeders onboard.