Can you be more specific about the broad-based ETFs you have in mind? I wasn't clear whether you are referring to broad-based US equity ETFs like the total market ETFs (IYY) and (TMW), or global ETFs like (VEU).
My unedited answer;
I could sum up by saying the broader you go the more you give up in the context I mean. The broader you go the greater the likelihood that whatever you buy will have a higher correlation to something like SPY. So as far as foreign goes something like EFA blends away the various attributes of the component countries. EFA has a higher correlation to every country fund I've ever looked at. One big reason to invest in foreign is to capture diversification for your US holdings, to me this means finding countries with as little in common with the US as possible which gets blended away in EFA.
As for domestic (US as this is where I'm based) and buying things like SPY, or the Russell 1000; my thoughts all along have been that these types of indexes won't work for the foreseeable future. That has been correct for a while and I believe will continue to be the case as my thesis has been the US is a less compelling investment destination such that the broad averages will have price appreciation below "normal," not an Armageddon scenario mind you, but maybe in ten years we look back on 3-5% annualized not 9% or whatever number we used to get.
Investors had a chance to add a lot of value to US portfolios during the last decade by building portfolios at the sector level but avoiding or underweighting sectors that grew to be larger than 20% of the S&P 500 (tech ten years ago and financials six or seven years ago) which is something I wrote about frequently before the crisis. Unfortunately with no sector that large now my opinion here is based more on a weak outlook for the US (too much debt, seriously damaged housing market, terrible employment picture, entitlement programs and the desperate measures taken by the Fed and the US gov't thus far.
I've navigated the last seven years (which how long I've been in this part of the business) on the premise that success will come from making sector decisions, country selections and incorporating themes into client portfolios. I expect this, that is making very narrow decisions, to continue to be the way to go for a long time into the future.
Now for something completely unrelated but fascinating (to me anyway). The new season of Alaska State Troopers started on Sunday Night on the Nat Geo channel; no DVD coming for this post.
One of the segments was about the little village of Diomede which is on a tiny island that off of Nome and on the Bering Strait. Apparently 117 people live there, what you see pictured to the left is the town. In the winter it is possible to walk out over the Strait two miles to Russian soil, or maybe just ice.
There are plenty of difficult ways to get on in life but the idea of being a 45 minute plane ride from Nome is difficult to imagine but still fascinating. When the show was filming there the temperature was about 50 below.