(Reuters) - Alphabet Inc GOOGL.O might win the market cap battle against Apple Inc AAPL.O, but will it win the war?

Maybe not.

The median share price forecast of 31 analysts who raised price targets after Alphabet reported strong results on Monday was $924, suggesting that the company formerly known as Google could be valued at $628 billion in the next 12 months.

Apple, tracked by 49 analysts, would be valued at $748.5 billion, at the current median price target of $135.

That’s not all.

A look at the most bullish price targets on the companies’ shares shows that Alphabet is expected to be valued at $734 billion in the next 12 months, while Apple could hit $1.10 trillion - making it the first publicly listed company ever to be worth more than $1 trillion.

Billionaire investor Carl Icahn, an Apple investor, said in May that the iPhone maker was “dramatically undervalued” and should trade at $240 per share. At that price, the company would be valued at about $1.30 trillion.

Alphabet easily beat Wall Street’s forecasts, helped by strong mobile advertising sales.

Alphabet’s shares rose as much as 4.4 percent to $804.50 on Tuesday, valuing the company at $546.50 billion, making it the world’s most valuable company - for now.

Letters spell the word "Alphabet" as they are seen on a computer screen with a Google search page in this photo illustration taken in Paris, France, August 11, 2015. REUTERS/Pascal Rossignol

Apple shares fell 1.2 percent to $95.28, giving the company a market capitalization of $528 billion.

Alphabet, which rejigged its operating structure last year to separate its core Google business from its so-called “moonshots” also broke out results for these operations for the first time on Monday.

BULLISH ON BOTH

Sustaining the lead could be tough, though.

The two tech giants have long wrestled for the top spot, as the likes of IBM IBM.N have declined.

Once allies, they fell out after Google launched its own Android mobile operating system in 2008.

Alphabet’s stock has surged 43 percent in the past year.

Apple, on the other hand, has struggled due to softening demand for its signature iPhone, especially in China, and the apparent lack of another blockbuster product in its pipeline.

Apple’s shares fell last week after the company reported disappointing results and have yet to recover.

Still Apple - whose stock has fallen about 18 percent in the past year - has an upcoming catalyst in the form of the iPhone 7 launch in September. That could spur sudden growth.

Alphabet is expected to gain more gradually from growth in mobile search and monetization of YouTube.

To be sure, analysts remain bullish on both stocks.

No analyst rates either stock a “sell”.

Apple shares trade at 10.59 times forward 12-month earnings versus Alphabet’s 22.47, among the most expensive in the tech sector.

“We think the current re-rating in GOOGL shares is two-thirds of the way complete and is likely to grind to $1000+,” Deutsche Bank analyst Ross Sandler wrote in a client note.

Sandler, the most bullish analyst on Alphabet, raised his price target on the stock to $1,080 from $900 on Tuesday.

Drexel Hamilton analyst Brian White is the most bullish on Apple stock, with a target of $200.