I don't think of a specific comparison but things like American vs National baseball remind me a bit of rugby. With NL you try to (or used to) "manufacture runs" vs (say) bringing in the DH fence blaster.
There are a lot of sites that explain the differences (union is slower due to "set plays" and has more players, while league has less players and moves faster). Some of the more idiosyncratic aspects are interesting.
There are concerns in the UK that while league play would appeal to more fans, those extra fans would also be more inclined toward the NFL as it penetrates UK sports. The more plodding union game might be better for rugby preservation (and union has a bigger following).
Union is the more traditional game that's played at Oxford, Sandhurst, West Point and in US D1. in UK, rugby is the more aristocratic game compared to soccer. Union is considered more upper-class than league - which is often defamed as more likely to be home to lower class, northern, wife beaters.
Union players can be bigger because they dont have to run quite as much. Roughly speaking, league has more of a continuous soccer play element while union sets-up more like US football.
In any case though, both involve a lot of running compared to football. If a US player build-up strength and mass for fall football, he would lose substantial bit of those playing rugby in the spring. I actually did that for a couple of years. You run so much in rugby that you dont really pop people that hard because you're always half-gassed
