There's only a few things to say...
All but 2 of the shards use the same ruleset.
that is, PvP only in Felucca facet (except, between alliance-mates and warring guild fights can occur on all facets).
These shards have insurance, that allows you to protect your items.
They also have NPCs that you can train skill up to 40 from, for most skills.
Atlantic is probably the busiest of the North American shards. Probably has the most active PvP on a regular basis, simply from population, but the other Eastern US shards also are fairly active for PvP. The West coast ones are fairly quiet, PvP-wise, but have spurts where one or two shards have active PvP going large-scale (some guilds like transferring from shard to shard, to fight)
Oceania is the shard for Australians & Kiwis
Europe has two shards (Europa and Drachenfels)
The Asian shards are really busy, but can be unfriendly to people that don't speak their language(s) (Chinese, Japanese and Korean shards)
The special shards are Siege Perilous and Mugen; both are limited to 1 character each.
Siege does not have Trammel at all, does not have insurance, the NPCs don't buy items (nor do they train skills), and PvP is available everywhere.
Mugen is oriented towards the Pacific players, and has the Trammel landmass, but is otherwise identical to Siege (and IIRC its trammel has PvP as well).