Having visited both Piccadilly and Victoria on an ad-hoc basis since the mid-1980s I would opine the following.
Both stations in the 1980s were dingy affairs. The main entrance to Piccadilly was claustrophobic and did nothing to welcome you to Manchester after arriving in the impressive trainshed - London Kings Cross offered a comparable 'welcome' to London at the time - and for some reason I always hatred the underpass to the through platforms at Victoria. Plts 13/14 at Piccadilly were horrendous and at the time, the trains serving them weren't any better unless you were lucky enough to catch a cl-303.
Unfortunately, BR did Victoria a great disservice when it built the Windsor Link lines and tried to push as many through services as possible through Piccadilly - was the ultimate aim to give Manchester a single main station and make Victoria a suburban terminus a la Moor Street (Birmingham)? Thankfully, if this was the aim, they didn't succeed and through services via Victoria were retained. However, imo the arena should never have been allowed to be built on top of Victoria in the way it was and I'm thankful that I've never had to use the through platforms since it's construction. If I ever need to, it will be a case of wait in the bar and head for the platform as late as possible.
In terms of the current stations, whilst the entrance to Piccadilly, and access to plts 13/14 is vastly better than it used to be, I find the mini shopping mall somewhat claustrophobic and the bar at Victoria is better than that at Piccadilly. Victoria is also better located for downtown shopping and drinking and has a more convenient interchange with the trams.
Unfortunately, my train service to Manchester is somewhat inconstant in that, although most trains go to Piccadilly, a few go to Victoria. Personally, I'd send all trains from the North Cheshire line into Victoria and if that means losing the direct link to the Airport (Edit: it does) then so be it - the detour via Earlstown makes the journey time uncompetitive with the M56.