A little out of my league here, but as I recall...
In wargaming terms, I believe they should be classed as 'Household' or at the very least 'Retinue' troops. They were full time soldiers and paid at the same rates as mounted archers (8d) after all. Henry VII had 50 archers in his original guard, which Henry VIII doubled in 1510, if I recall correctly. These were archers, but armed with halberds (or partizans, depending on your source) - It had been common practice in Calais and Berwick etc, to provide halberds to archers for 'watch and ward', while they retained their bows for battle. Henry VIII added a further 500 archers for the French Campaign, along with 50 'Harquebusiers' and 100 mounted archers.
This seems to say the same;
http://yeomenoftheguard.com/detailed.htm#henryviii In this context I'd assume that they would fulfil the same role as a present day Guards Battalion. They would be skilled archers and likely be selected from numerous applicants for very few open places in peace time. For the war though, standards might be dropped a tad, but they would still test the skills of the archers before signing them up to pad the corps out to its 600.
In comparison to the other troops though, they'd be somewhat of an elite, even if just in their own minds.
