Walking might be difficult for the unitiated, since the route is a bit convoluted.
Inter-terminal bus or Skytrain is definitely quicker.
The former does tend to get very full and I concur with your comments about lots of PAX with ridiculous amounts of luggage struggling to get on!
There is also a public bus route
#61 which goes from the far end of T2 arrivals level every 15 mins - it is nothing like as crowded and basically follows the same route as the inter-terminal bus - in theory you would need to purchase a ticket for this.
When transferring T2 to T1 at FRA, it really depends on what your intentions are - if you want to catch the S-Bahn, regional or express train, then use the bus, but if you are transferring to another flight then use the Skytrain, which will keep you on the airport side of the complex rather than the rail/road side.
And if you are HBO and are transferring to a Schengen-internal Lufthansa flight departing Termial 1A and you already have a boarding card,then stay on the Skytrain at Terminal 1B until Terminal 1A (final stop) where security is a breeze!