Nah, they're just the teams I've gravitated towards. Liverpool doesn't have a top flight union team as the north is really League territory. Orrel is the nearest union club of any note.
In League St Helens is probably the closest club to Liverpool and I believe a few people on here support them. As mentioned, in the north of England League is more common than Union. It's played in the summer as well so you can pick a team and follow them through the season from the start in Feb/March. Saints are probably the best team at the moment, although Leeds won the title last year.
As for the differences between League and Union. The obvious one is that League has 13 players, Union 15 (Union has 2 locks, primarily used in the lineout - League doesn't have lineouts so therefore doesn't need the locks).
The main difference though is in the tackle area. In League each team has 6 tackles in posession, so the tackle area is uncontested. In Union teams can have as many tackles as they want, but the tackle area is contested, either in mauls (when the players are tackled on their feet), or rucks (when they players are tackled on the floor).
Union also tends to place greater emphasis on set pieces, such as scrums and lineouts. This results in a more prominent kicking game and a higher penalty count. In League there are no lineouts and scrums are uncontested (ie merely a means of restarting the game) so greater emphasis is placed on scoring tries.
That's the main differences. Where they become similar is in the best teams dominating the tsecuring a quick play of the ball (ie the time between the player being tackled, getting to his feet and starting again). This then allows the next wave of attack to be madeackle area. In League for instance St Helens have become expert at against a defensive line that has less time to align itself.
Likewise in Union New Zealand are the masters at securing quick ball. As soon as the player is tackled, the opponent is cleared from the ruck very quickly, allowing the scrum half to get the next wave of attack going very quickly.
Of course the flip side of this is that when defending if you can slow the play of the ball down it helps you tremendously. Again New Zealand are very good at this, with their captain Richie McCaw the best in the world. In League you'll see tacklers turning players onto their backs to make it harder for them to regain their feet, and you often see penalties awarded for holding the player down for too long.
That about sums it up I think. The games are generally cheaper to go to than football matches so pop along, see what you think.