• Seedcamp has only had one large exit (> $1M), whereas YC has had more than a dozen.
• YC funds more companies per batch now than Seedcamp has funded total.
• I'd guess that there's a two order of magnitude gap in the portfolio worth of YC vs. Seedcamp right now (given that AirBnb and Dropbox together have a valuation around the $6 billion mark).
Seedcamp on the other hand is more inclusive and network oriented -- it's borders are a lot fuzzier, so it's influenced a lot of companies (mine included) that weren't funded by it.
Of course, there are many many other differences but these are the most obvious.
In contrast, Seedcamp runs day events around Europe throughout the year which lead up to the annual Seedcamp Week from which a number of companies "win" and get the investment. Having been part of the 2009 batch and getting an investment with http://www.serverdensity.com I didn't even move to London (although I am there now) and there was much less structure than YC has (not a bad thing).
I believe the months following the Seedcamp Week are now more involved for the winning teams but the differences are still there. Perhaps that's why many Seedcamp winners tend to already have a product built, revenue and customers (of course there are many YC teams now in the same position).
I don't see them as competitors, just different approaches to a similar idea. You have a choice who you apply to knowing this.
Y combinator is not present in Europe, so Seedcamp can enjoy vastly more mind share than maybe its model merits.
We wanted to make a service similar to what Zaarly has created. When evaluating whether we wanted to compete, we did not take into account that it may take Zaarly years to get to Europe and we could still enjoy first mover advantage in a massive geography (there are competitors, but we consider them to not 'get it').
Same with Seedcamp - FIVE years and few have really come along to do something better. Seedcamp is the accelerator we aspire to have notice us. Would that change if YC came to Europe/London? Do Seedcamp have a local knowledge/network advantage that would be unshareable?
To those comments about zero sum - it is like wanting the FT to report on your news, but having to settle for a financial blog read by only a few thousand.
Bigger really is better and that applies broadly to accelerators, start ups and general economies of scale. Brand awareness often requires scale, which comes as a result of time and effort.
For now YC is way ahead of any competition.