sancho
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It says it can detect a fight sized aircraft at 350KM, but if its a bigger sized aircraft, it can be detected at longer ranges.
Instrument range would most probably mean the maximum range where the radar waves can travel and have detection capability. A ship at sea can most probably be detected at much larger range, similarly a big aircraft would be detected at more then 350Km range.
Now the specifications of this radar is not even clear, that what it means fighter sized aircraft it can detect, is it with RCS of 1m2, 3m2 or what. If they mean fighter sized aircraft with RCS 1m2 at 350KM, then definitely it can detect larger RCS aircraft at more then 350KM.
But the detection of how much RCS fighter sized aircraft are classified.
Instrumental range is the range it can detect targets via ESM, that means it gathers some signals, but can't identify, or track it in that range. The 350Km range for fighter sized targets instead are the actual radar range and it is more likely that they are talking about targets with a RCS of 3 - 5 m². Cruise missiles are often quoted at 1m² and the detection for such targets are far less.
The most reliable source for the Erieye, is still this Saab Graphic:
http://pakbee.com/wp-content/uploads/2009/12/Saab-2000-Pakistan-Air-Force-2.jpg
As you can see it detects cruise missiles only in around 180Km, ships around 270Km and fighters (in normal altitudes) as mentioned before in 350Km range.
The only directly comparable figur from Beriev, the manufacturer of the A50 (with Russian radar system) is the detection of cruise missiles with a RCS of 1m²:
Detection range for: cruise missiles (S1m2), km 215
Beriev Aircraft Company
So even the Russian version seems to offer some advantages in detection compared to Swedish, sadly there are not reliable sources for the A50 Phalcon.