The successor to the Wii will obviously have significantly better third party support upon release, with a significantly stronger line-up of games in conventional genres using well known IPs developed by strong developers; and if the system is similarly popular, having more quality core games will ensure that these genres sell well by attracting more core gamers (or at least attracting their attention better).
There are two main reasons for this:
First off, third party publishers are not going to risk “missing out” on the success of another Nintendo platform after they ignored the DS and Wii to their own detriment; and, rather than ignore potential customers for 3 years to throw them a few scraps and claim that they must have never been interested in those experience in the first place, there will probably be a significant effort to produce games across all genres and let the customers decide what they want.
The second reason comes down to processing power and performance. I don’t think that either Sony or Microsoft will produce a console that launches at a price higher than $400, and I doubt they would produce systems which consumed as much energy and ran as hot as their current consoles did. At the same time, for at least the first 2 to 3 years of the next generation many/most multiplatform games will be released using the current HD consoles as the game’s minimum requirements. Now, with a brand new $35 graphics card surpassing the performance of the HD consoles at retail (with both manufacturer and retailer profit) I doubt Nintendo will have difficulty producing a console that isn’t powerful enough to receive mutli-platform games in the next generation.