LHR has got 4 different terminals, which makes connecting rather complicated even when you transfer within BA or Oneworld flights, the connecting takes long time, there are partly old facilities and very, very long ways to walk (in huge airports you have to walk some mile, i know, but Heathrow beats them all). On the other hand LHR can offer many, many flights and rather huge shopping areas.
CDG(2) is a new, nice and modern airport, which offers a huge number of connecting possibilities (within AF). But with the growing facilities (additional terminals like 2E/F) new problems like the very long ways etc. are appearing. But altogether, there´s no doubt, CDG is an airport with a big future. I have been only to CDG1, not to CDG2, so i can´t judge about it.
AMS has a "all in one terminal" with a huge shopping and food area. Very comfortable connections there. FRAs LH/Star Alliance parts A and B are really nice now, after the redesigning. Both offer a wide range of flight with FRA on the top.
I can´t say much about the convenience of LGW, MAD and FCO. Especially MAD will grow in its importance as a huge transit airport, of course also LGW and FCO will do.
MUC, at the moment a "medium" player in Europe, will grow up and become another big player, thanks to LHs expansion in the coming years. Despite MUC is a new, modern and very functional airport with a really nice architecture, there are some problems here at the moment due to the recently huge growth, like a overcrowded terminal in peak hours, few boarding bridges, rather few shops and restaurants within the departure area. The current terminal was designed for O&D-traffic (decentral check-in and baggage-claim) and not for a huge hub&spoke operation as LH has built up in MUC. Only one and a half year to go, then the 1.2 billion$ Terminal 2 will be opened in summer 2003, which will solve all the small problems. This facility will offer enough space to grow exclusively for the Star Alliance partners and LH. The new terminal will be designed especially for the needs of connecting passengers (shopping areas, food courts, service centers for ticketing and check-in, huge Star Alliance lounges, moving walkways, comfortable calm seating areas etc. etc.). At this time the other airlines will also get more space to grow in the half-empty "old" terminal. I´m sure, MUC will be among the top airports for connecting passengers in Europe as well as of course for the "normal" O&D pax.
Last but not least i want to mention CPH, ZRH, MXP, BRU and VIE. All are different sized hubs for their homebase carriers with VIE the smallest and ZRH the biggest.