Edinburgh-based Scottish Mortgage, under manager James Anderson, has long taken an unconventional view of the market, investing in stocks such as Chinese online search engine Baidu, which are shunned by many fund managers as too expensive or too risky.
Meanwhile, Alliance Trust, which typically adopts a more cautious approach, said its portfolio had shrunk 0.6% in the three months to the end of September as its bias towards US equities held it back.
After seeing its share price tip over the £10 mark for the first time in its 104-year history in recent days, Scottish Mortgage now has a market worth of £2.546 billion, a sliver ahead of Alliance Trust at £2.539bn, based on last night's closing prices.
Alliance Trust, which dates back to 1888, remains bigger in terms of assets.
Stephen Peters, analyst at Charles Stanley, said: "The key difference between the two is in investment approach."
He added: "The way in which James operates is a pure version of the Baillie Gifford philosophy. It is very long term, very binary.
"You have some winners in the world and you have the rest and he is trying to pick the winners."
Despite some volatile periods, the result over five years to the end of September was that Scottish Mortgage's net asset value is up 104% and the share price 126% ahead.
Mr Anderson has been on sabbatical since the summer, ostensibly to write a book, leaving the trust in the hands of deputy Tom Slater. Nevertheless, such has been the continued popularity of its shares, the trust's directors said they could release more if they moved to a premium to net asset value.
Its managers said that while investors remained concerned about the removal of central bank stimulus measures, economies such as the US, Germany and the UK were recovering and the likes of China were still growing relatively fast.
"This is probably the strand that has most impact on confidence and also on individual companies' operational plans and future returns," they wrote.
Alliance Trust, which is headed by Katherine Garrett Cox, said: "The equity portfolio has been affected by the relative under-performance of the US market - in which we are more heavily invested than at any time in over 20 years - over the summer, when compared to other major markets.
"We continue to see the companies in which we are invested as well-positioned for the medium to long term."